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Yıl 2020, Cilt: 28 Sayı: 28, 75 - 97, 14.07.2020

Maryam Hamıdızadeh Ebrahim Hashemı Armando Reyes

https://doi.org/10.24330/ieja.768178
Cited By: 7

Öz

Kaynakça

  • A. Alhevaz and A. Moussavi, On skew Armendariz and skew quasi-Armendariz modules, Bull. Iranian Math. Soc., 38(1) (2012), 55-84.
  • D. F. Anderson and A. Badawi, Von Neumann regular and related elements in commutative rings, Algebra Colloq., 19(1) (2012), 1017-1040.
  • S. Annin, Associated primes over Ore extension rings, J. Algebra Appl., 3(2) (2004), 193-205.
  • J. Apel, Grobnerbasen in Nichtkommutativen Algebren und ihre Anwendung, PhD Thesis, Leipzig, Karl-Marx-Univ., 1988.
  • V. A. Artamonov, Derivations of skew PBW extensions, Commun. Math. Stat., 3(4) (2015), 449-457.
  • V. A. Artamonov, O. Lezama and W. Fajardo, Extended modules and Ore extensions, Commun. Math. Stat., 4(2) (2016), 189-202.
  • A. Badawi, On abelian $\pi$-regular rings, Comm. Algebra, 25(4) (1997), 1009-1021.
  • V. V. Bavula, Generalized Weyl algebras and their representations, (Russian) Algebra i Analiz, 4(1) (1992), 75-97; translation in St. Petersburg Math. J., 4(1) (1993), 71-92.
  • T. Becker and V.Weispfenning, Grobner Bases, A Computational Approach to Commutative Algebra, Graduate Texts in Mathematics, 141, Springer-Verlag, New York, 1993.
  • H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc., 2 (1970), 363-368.
  • A. D. Bell and K. R. Goodearl, Uniform rank over differential operator rings and Poincare-Birkhoff-Witt extensions, Paci c J. Math., 131(11) (1988), 13-37.
  • G. F. Birkenmeier, H. E. Heatherly and E. K. Lee, Completely prime ideals and associated radicals, in Proc. Biennial Ohio State - Denison Conf., Granville, USA, (1992), eds. S. K. Jain and S. T. Rizvi, World Sci. Publ., River Edge, New Jersey, (1993), 102-129.
  • K. A. Brown and K. R. Goodearl, Lectures on Algebraic Quantum Groups, Advanced Courses in Mathematics, CRM Barcelona, Birkhauser Verlag, Basel, 2002.
  • J. L. Bueso, J. Gomez-Torrecillas and F. J. Lobillo, Homological computations in PBW modules, Algebr. Represent. Theory, 4(3) (2001), 201-218.
  • J. L. Bueso, J. Gomez-Torrecillas and A. Verschoren, Algorithmic Methods in Non-commutative Algebra, Applications to Quantum Groups, Mathematical Modelling: Theory and Applications, 17, Kluwer Academic Publishers, Dordrecht, 2003.
  • W.-X. Chen and S.-Y. Cui, On weakly semicommutative rings, Commun. Math. Res., 27(2) (2011), 179-192.
  • M. Contessa, On certain classes of pm-rings, Comm. Algebra, 12(11-12) (1984), 1447-1469.
  • C. Gallego and O. Lezama, Grobner bases for ideals of $\sigma$-PBW extensions, Comm. Algebra, 39(1) (2011), 50-75.
  • M. Habibi, A. Moussavi and A. Alhevaz, The McCoy condition on Ore extensions, Comm. Algebra, 41(1) (2013), 124-141.
  • E. Hashemi, Compatible ideals and radicals of Ore extensions, New York J. Math., 12 (2006), 349-356.
  • E. Hashemi, M. Hamidizadeh and A. Alhevaz, Some types of ring elements in Ore extensions over noncommutative rings, J. Algebra Appl., 16(11) (2017), 1750201 (17 pp).
  • E. Hashemi, K. Khalilnezhad and A. Alhevaz, $(\Sigma, \Delta)$-Compatible skew PBW extension ring, Kyungpook Math. J., 57(3) (2017), 401-417.
  • E. Hashemi, K. Khalilnezhad and A. Alhevaz, Extensions of rings over 2-primal rings, Matematiche (Catania), 74(1) (2019), 141-162.
  • E. Hashemi, K. Khalilnezhad and H. Ghadiri, Baer and quasi-Baer properties of skew PBW extensions, J. Algebr. Syst., 7(1) (2019), 1-24.
  • E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar., 107(3) (2005), 207-224.
  • E. Hashemi, A. Moussavi and H. H. Seyyed Javadi, Polynomial Ore extensions of Baer and p.p.-rings, Bull. Iranian Math. Soc., 29(2) (2003), 65-86.
  • Y. Hirano, Some studies on strongly $\pi$-regular rings, Math. J. Okayama Univ., 20(2) (1978), 141-149.
  • C. Y. Hong, N. K. Kim and T. K. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra, 151(3) (2000), 215-226.
  • C. Y. Hong, T. K. Kwak and S. T. Rizvi, Rigid ideals and radicals of Ore extensions, Algebra Colloq., 12(3) (2005), 399-412.
  • A. P. Isaev, P. N. Pyatov and N. Rittenberg, Diffusion algebras, J. Phys. A., 34 (2001), 5815-5834.
  • A. Kandri-Rody and V. Weispfenning, Noncommutative Grobner bases in algebras of solvable type, J. Symbolic Comput., 9(1) (1990), 1-26.
  • P. Kanwar, A. Leroy and J. Matczuk, Idempotents in ring extensions, J. Algebra, 389(1) (2013), 128-136.
  • P. Kanwar, A. Leroy and J. Matczuk, Clean elements in polynomial rings, Contemp. Math., 634 (2015), 197-204.
  • O. A. S. Karamzadeh, On constant products of polynomials, Int. J. Math. Edu. Technol., 18 (1987), 627-629.
  • J. Krempa, Some examples of reduced rings, Algebra Colloq., 3(4) (1996), 289-300.
  • T. Y. Lam, A First Course in Noncommutative Rings, 2nd ed., Graduate Texts in Mathematics, Vol. 131, Springer-Verlag, New York, 2001.
  • O. Lezama, J. P. Acosta and A. Reyes, Prime ideals of skew PBW extensions, Rev. Un. Mat. Argentina, 56(2) (2015), 39-55.
  • O. Lezama and C. Gallego, d-Hermite rings and skew PBW extensions, Sao Paulo J. Math. Sci., 10(1) (2016), 60-72.
  • O. Lezama and A. Reyes, Some homological properties of skew PBW extensions, Comm. Algebra, 42(3) (2014), 1200-1230.
  • Z. K. Liu and R. Y. Zhao, On weak Armendariz rings, Comm. Algebra, 34(7) (2006), 2607-2616.
  • M. Louzari and A. Reyes, Minimal prime ideals of skew PBW extensions over 2-primal compatible rings, Rev. Colombiana Mat., 54(1) (2020), 27-51.
  • G. Marks, A taxonomy of 2-primal rings, J. Algebra, 266(2) (2003), 494-520.
  • J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Graduate Studies in Mathematics, 30, American Mathematical Society, Providence, RI, 2001.
  • W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), 269-278.
  • W. K. Nicholson and Y. Zhou, Clean rings: A survey, in Advances in Ring Theory, World Sci. Publ., Hackensack, NJ, (2005), 181-198.
  • A. Nino, M. C. Ramirez and A. Reyes, Associated prime ideals over skew PBW extensions, Comm. Algebra, (2020), https://doi.org/10.1080/00927872.2020.1778012.
  • A. Nino and A. Reyes, Some ring theoretical properties of skew Poincare-Birkhoff-Witt extensions, Bol. Mat., 24(2) (2017), 131-148.
  • O. Ore, Theory of non-commutative polynomials, Ann. of Math. Second Series, 34(3) (1933), 480-508.
  • A. Reyes, Skew PBW extensions of Baer, quasi-Baer, p.p. and p.q.-rings, Rev. Integr. Temas Mat., 33(2) (2015), 173-189.
  • A. Reyes, $\sigma$-PBW extensions of skew $\Pi$-Armendariz rings, Far East J. Math. Sci., 103(2) (2018), 401-428.
  • A. Reyes, Armendariz modules over skew PBW extensions, Comm. Algebra, 47(3) (2019), 1248-1270.
  • A. Reyes and C. Rodriguez, The McCoy condition on skew PBW extensions, Commun. Math. Stat., (2019), https://doi.org/10.1007/s40304-019-00184-5.
  • A. Reyes and H. Suarez, Armendariz property for skew PBW extensions and their classical ring of quotients, Rev. Integr. Temas Mat., 34(2) (2016), 147-168.
  • A. Reyes and H. Suarez, Bases for quantum algebras and skew Poincare-Birkhoff-Witt extensions, Momento, 54(1) (2017), 54-75.
  • A. Reyes and H. Suarez, PBW bases for some 3-dimensional skew polynomial algebras, Far East J. Math. Sci., 101(6) (2017), 1207-1228.
  • A. Reyes and H. Suarez, $\sigma$-PBW extensions of skew Armendariz rings, Adv. Appl. Clifford Algebr., 27(4) (2017), 3197-3224.
  • A. Reyes and H. Suarez, A notion of compatibility for Armendariz and Baer properties over skew PBW extensions, Rev. Un. Mat. Argentina, 59(1) (2018), 157-178.
  • A. Reyes and Y. Suarez, On the ACCP in skew Poincare-Birkhoff-Witt extensions, Beitr. Algebra Geom., 59(4) (2018), 625-643.
  • A. Reyes and H. Suarez, Skew Poincare-Birkhoff-Witt extensions over weak zip rings, Beitr. Algebra Geom., 60(2) (2019), 197-216.
  • A. Reyes and H. Suarez, Radicals and Köthe's conjecture for skew PBW extensions, Commun. Math. Stat., (2019), https://doi.org/10.1007/s40304-019-00189-0.
  • A. L. Rosenberg, Noncommutative Algebraic Geometry and Representations of Quantized Algebras, Mathematics and Its Applications, Vol. 330, Kluwer Academic Publishers Group, Dordrecht, 1995.
  • G. Y. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc., 184 (1973), 43-60.
  • H. Suarez, O. Lezama and A. Reyes, Calabi-Yau property for graded skew PBW extensions, Rev. Colombiana Mat., 51(2) (2017), 221-239.
  • H. Suarez and A. Reyes, A generalized Koszul property for skew PBW extensions, Far East J. Math. Sci., 101(2) (2017), 301-320.

A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS

Yıl 2020, Cilt: 28 Sayı: 28, 75 - 97, 14.07.2020

Maryam Hamıdızadeh Ebrahim Hashemı Armando Reyes

https://doi.org/10.24330/ieja.768178
Cited By: 7

Öz

For a skew PBW extension over a right duo compatible ring, we characterize several kinds of their elements such as units, idempotent, von Neumann regular, $\pi$-regular and the clean elements. As a consequence of our treatment, we extend several results in the literature for Ore extensions and commutative rings. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

Anahtar Kelimeler

Right duo ring skew PBW extension idempotent element unit element von Neumann regular element clean element

Kaynakça

  • A. Alhevaz and A. Moussavi, On skew Armendariz and skew quasi-Armendariz modules, Bull. Iranian Math. Soc., 38(1) (2012), 55-84.
  • D. F. Anderson and A. Badawi, Von Neumann regular and related elements in commutative rings, Algebra Colloq., 19(1) (2012), 1017-1040.
  • S. Annin, Associated primes over Ore extension rings, J. Algebra Appl., 3(2) (2004), 193-205.
  • J. Apel, Grobnerbasen in Nichtkommutativen Algebren und ihre Anwendung, PhD Thesis, Leipzig, Karl-Marx-Univ., 1988.
  • V. A. Artamonov, Derivations of skew PBW extensions, Commun. Math. Stat., 3(4) (2015), 449-457.
  • V. A. Artamonov, O. Lezama and W. Fajardo, Extended modules and Ore extensions, Commun. Math. Stat., 4(2) (2016), 189-202.
  • A. Badawi, On abelian $\pi$-regular rings, Comm. Algebra, 25(4) (1997), 1009-1021.
  • V. V. Bavula, Generalized Weyl algebras and their representations, (Russian) Algebra i Analiz, 4(1) (1992), 75-97; translation in St. Petersburg Math. J., 4(1) (1993), 71-92.
  • T. Becker and V.Weispfenning, Grobner Bases, A Computational Approach to Commutative Algebra, Graduate Texts in Mathematics, 141, Springer-Verlag, New York, 1993.
  • H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc., 2 (1970), 363-368.
  • A. D. Bell and K. R. Goodearl, Uniform rank over differential operator rings and Poincare-Birkhoff-Witt extensions, Paci c J. Math., 131(11) (1988), 13-37.
  • G. F. Birkenmeier, H. E. Heatherly and E. K. Lee, Completely prime ideals and associated radicals, in Proc. Biennial Ohio State - Denison Conf., Granville, USA, (1992), eds. S. K. Jain and S. T. Rizvi, World Sci. Publ., River Edge, New Jersey, (1993), 102-129.
  • K. A. Brown and K. R. Goodearl, Lectures on Algebraic Quantum Groups, Advanced Courses in Mathematics, CRM Barcelona, Birkhauser Verlag, Basel, 2002.
  • J. L. Bueso, J. Gomez-Torrecillas and F. J. Lobillo, Homological computations in PBW modules, Algebr. Represent. Theory, 4(3) (2001), 201-218.
  • J. L. Bueso, J. Gomez-Torrecillas and A. Verschoren, Algorithmic Methods in Non-commutative Algebra, Applications to Quantum Groups, Mathematical Modelling: Theory and Applications, 17, Kluwer Academic Publishers, Dordrecht, 2003.
  • W.-X. Chen and S.-Y. Cui, On weakly semicommutative rings, Commun. Math. Res., 27(2) (2011), 179-192.
  • M. Contessa, On certain classes of pm-rings, Comm. Algebra, 12(11-12) (1984), 1447-1469.
  • C. Gallego and O. Lezama, Grobner bases for ideals of $\sigma$-PBW extensions, Comm. Algebra, 39(1) (2011), 50-75.
  • M. Habibi, A. Moussavi and A. Alhevaz, The McCoy condition on Ore extensions, Comm. Algebra, 41(1) (2013), 124-141.
  • E. Hashemi, Compatible ideals and radicals of Ore extensions, New York J. Math., 12 (2006), 349-356.
  • E. Hashemi, M. Hamidizadeh and A. Alhevaz, Some types of ring elements in Ore extensions over noncommutative rings, J. Algebra Appl., 16(11) (2017), 1750201 (17 pp).
  • E. Hashemi, K. Khalilnezhad and A. Alhevaz, $(\Sigma, \Delta)$-Compatible skew PBW extension ring, Kyungpook Math. J., 57(3) (2017), 401-417.
  • E. Hashemi, K. Khalilnezhad and A. Alhevaz, Extensions of rings over 2-primal rings, Matematiche (Catania), 74(1) (2019), 141-162.
  • E. Hashemi, K. Khalilnezhad and H. Ghadiri, Baer and quasi-Baer properties of skew PBW extensions, J. Algebr. Syst., 7(1) (2019), 1-24.
  • E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar., 107(3) (2005), 207-224.
  • E. Hashemi, A. Moussavi and H. H. Seyyed Javadi, Polynomial Ore extensions of Baer and p.p.-rings, Bull. Iranian Math. Soc., 29(2) (2003), 65-86.
  • Y. Hirano, Some studies on strongly $\pi$-regular rings, Math. J. Okayama Univ., 20(2) (1978), 141-149.
  • C. Y. Hong, N. K. Kim and T. K. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra, 151(3) (2000), 215-226.
  • C. Y. Hong, T. K. Kwak and S. T. Rizvi, Rigid ideals and radicals of Ore extensions, Algebra Colloq., 12(3) (2005), 399-412.
  • A. P. Isaev, P. N. Pyatov and N. Rittenberg, Diffusion algebras, J. Phys. A., 34 (2001), 5815-5834.
  • A. Kandri-Rody and V. Weispfenning, Noncommutative Grobner bases in algebras of solvable type, J. Symbolic Comput., 9(1) (1990), 1-26.
  • P. Kanwar, A. Leroy and J. Matczuk, Idempotents in ring extensions, J. Algebra, 389(1) (2013), 128-136.
  • P. Kanwar, A. Leroy and J. Matczuk, Clean elements in polynomial rings, Contemp. Math., 634 (2015), 197-204.
  • O. A. S. Karamzadeh, On constant products of polynomials, Int. J. Math. Edu. Technol., 18 (1987), 627-629.
  • J. Krempa, Some examples of reduced rings, Algebra Colloq., 3(4) (1996), 289-300.
  • T. Y. Lam, A First Course in Noncommutative Rings, 2nd ed., Graduate Texts in Mathematics, Vol. 131, Springer-Verlag, New York, 2001.
  • O. Lezama, J. P. Acosta and A. Reyes, Prime ideals of skew PBW extensions, Rev. Un. Mat. Argentina, 56(2) (2015), 39-55.
  • O. Lezama and C. Gallego, d-Hermite rings and skew PBW extensions, Sao Paulo J. Math. Sci., 10(1) (2016), 60-72.
  • O. Lezama and A. Reyes, Some homological properties of skew PBW extensions, Comm. Algebra, 42(3) (2014), 1200-1230.
  • Z. K. Liu and R. Y. Zhao, On weak Armendariz rings, Comm. Algebra, 34(7) (2006), 2607-2616.
  • M. Louzari and A. Reyes, Minimal prime ideals of skew PBW extensions over 2-primal compatible rings, Rev. Colombiana Mat., 54(1) (2020), 27-51.
  • G. Marks, A taxonomy of 2-primal rings, J. Algebra, 266(2) (2003), 494-520.
  • J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Graduate Studies in Mathematics, 30, American Mathematical Society, Providence, RI, 2001.
  • W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), 269-278.
  • W. K. Nicholson and Y. Zhou, Clean rings: A survey, in Advances in Ring Theory, World Sci. Publ., Hackensack, NJ, (2005), 181-198.
  • A. Nino, M. C. Ramirez and A. Reyes, Associated prime ideals over skew PBW extensions, Comm. Algebra, (2020), https://doi.org/10.1080/00927872.2020.1778012.
  • A. Nino and A. Reyes, Some ring theoretical properties of skew Poincare-Birkhoff-Witt extensions, Bol. Mat., 24(2) (2017), 131-148.
  • O. Ore, Theory of non-commutative polynomials, Ann. of Math. Second Series, 34(3) (1933), 480-508.
  • A. Reyes, Skew PBW extensions of Baer, quasi-Baer, p.p. and p.q.-rings, Rev. Integr. Temas Mat., 33(2) (2015), 173-189.
  • A. Reyes, $\sigma$-PBW extensions of skew $\Pi$-Armendariz rings, Far East J. Math. Sci., 103(2) (2018), 401-428.
  • A. Reyes, Armendariz modules over skew PBW extensions, Comm. Algebra, 47(3) (2019), 1248-1270.
  • A. Reyes and C. Rodriguez, The McCoy condition on skew PBW extensions, Commun. Math. Stat., (2019), https://doi.org/10.1007/s40304-019-00184-5.
  • A. Reyes and H. Suarez, Armendariz property for skew PBW extensions and their classical ring of quotients, Rev. Integr. Temas Mat., 34(2) (2016), 147-168.
  • A. Reyes and H. Suarez, Bases for quantum algebras and skew Poincare-Birkhoff-Witt extensions, Momento, 54(1) (2017), 54-75.
  • A. Reyes and H. Suarez, PBW bases for some 3-dimensional skew polynomial algebras, Far East J. Math. Sci., 101(6) (2017), 1207-1228.
  • A. Reyes and H. Suarez, $\sigma$-PBW extensions of skew Armendariz rings, Adv. Appl. Clifford Algebr., 27(4) (2017), 3197-3224.
  • A. Reyes and H. Suarez, A notion of compatibility for Armendariz and Baer properties over skew PBW extensions, Rev. Un. Mat. Argentina, 59(1) (2018), 157-178.
  • A. Reyes and Y. Suarez, On the ACCP in skew Poincare-Birkhoff-Witt extensions, Beitr. Algebra Geom., 59(4) (2018), 625-643.
  • A. Reyes and H. Suarez, Skew Poincare-Birkhoff-Witt extensions over weak zip rings, Beitr. Algebra Geom., 60(2) (2019), 197-216.
  • A. Reyes and H. Suarez, Radicals and Köthe's conjecture for skew PBW extensions, Commun. Math. Stat., (2019), https://doi.org/10.1007/s40304-019-00189-0.
  • A. L. Rosenberg, Noncommutative Algebraic Geometry and Representations of Quantized Algebras, Mathematics and Its Applications, Vol. 330, Kluwer Academic Publishers Group, Dordrecht, 1995.
  • G. Y. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc., 184 (1973), 43-60.
  • H. Suarez, O. Lezama and A. Reyes, Calabi-Yau property for graded skew PBW extensions, Rev. Colombiana Mat., 51(2) (2017), 221-239.
  • H. Suarez and A. Reyes, A generalized Koszul property for skew PBW extensions, Far East J. Math. Sci., 101(2) (2017), 301-320.
Toplam 64 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Maryam Hamıdızadeh Bu kişi benim

Ebrahim Hashemı Bu kişi benim

Armando Reyes Bu kişi benim

Yayımlanma Tarihi 14 Temmuz 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 28 Sayı: 28

Kaynak Göster

APA Hamıdızadeh, M., Hashemı, E., & Reyes, A. (2020). A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS. International Electronic Journal of Algebra, 28(28), 75-97. https://doi.org/10.24330/ieja.768178
AMA Hamıdızadeh M, Hashemı E, Reyes A. A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS. IEJA. Temmuz 2020;28(28):75-97. doi:10.24330/ieja.768178
Chicago Hamıdızadeh, Maryam, Ebrahim Hashemı, ve Armando Reyes. “A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS”. International Electronic Journal of Algebra 28, sy. 28 (Temmuz 2020): 75-97. https://doi.org/10.24330/ieja.768178.
EndNote Hamıdızadeh M, Hashemı E, Reyes A (01 Temmuz 2020) A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS. International Electronic Journal of Algebra 28 28 75–97.
IEEE M. Hamıdızadeh, E. Hashemı, ve A. Reyes, “A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS”, IEJA, c. 28, sy. 28, ss. 75–97, 2020, doi: 10.24330/ieja.768178.
ISNAD Hamıdızadeh, Maryam vd. “A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS”. International Electronic Journal of Algebra 28/28 (Temmuz 2020), 75-97. https://doi.org/10.24330/ieja.768178.
JAMA Hamıdızadeh M, Hashemı E, Reyes A. A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS. IEJA. 2020;28:75–97.
MLA Hamıdızadeh, Maryam vd. “A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS”. International Electronic Journal of Algebra, c. 28, sy. 28, 2020, ss. 75-97, doi:10.24330/ieja.768178.
Vancouver Hamıdızadeh M, Hashemı E, Reyes A. A CLASSIFICATION OF RING ELEMENTS IN SKEW PBW EXTENSIONS OVER COMPATIBLE RINGS. IEJA. 2020;28(28):75-97.

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Some remarks about minimal prime ideals of skew Poincaré-Birkhoff-Witt extensions
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