Research Article
BibTex RIS Cite

Year 2025, Early Access, 1 - 16

Sebastian Higuera Armando Reyes

https://doi.org/10.24330/ieja.1629334

Abstract

References

  • S. A. Annin, Associated and Attached Primes over Noncommutative Rings, Ph.D. Thesis, University of California, Berkeley, 2002.
  • S. A. Annin, Associated primes over Ore extension rings, J. Algebra Appl., 3(2) (2004), 193-205.
  • S. A. Annin, Couniform dimension over skew polynomial rings, Comm. Algebra, 33(4) (2005), 1195-1204.
  • S. A. Annin, Attached primes under skew polynomial extensions, J. Algebra Appl., 10(3) (2011), 537-547.
  • A. D. Bell and K. R. Goodearl, Uniform rank over differential operator rings and Poincare-Birkhoff-Witt extensions, Pacific J. Math., 131(1) (1988), 13-37.
  • P. A. A. B. Carvalho, S. A. Lopes and J. Matczuk, Double Ore extensions versus iterated Ore extensions, Comm. Algebra, 39(8) (2011), 2838-2848.
  • A. Chacon and A. Reyes, On the schematicness of some Ore polynomials of higher order generated by homogenous quadratic relations, J. Algebra Appl., (2025), 2550207 (19 pp).
  • P. M. Cohn, Quadratic extensions of skew fields, Proc. London Math. Soc. (3), 11 (1961), 531-556.
  • R. Diaz and E. Pariguan, On the $q$-meromorphic Weyl algebra, Sao Paulo J. Math. Sci., 3(2) (2009), 283-298.
  • F. Dumas, Sous-corps de fractions rationnelles des corps gauches de series de Laurent, Topics in Invariant Theory, Lecture Notes in Math., Springer, Berlin, 1478 (1991), 192-214.
  • C. Faith, Rings whose modules have maximal submodules, Publ. Mat., 39(1) (1995), 201-214.
  • W. Fajardo, C. Gallego, O. Lezama, A. Reyes, H. Suarez and H. Venegas, Skew PBW Extensions: Ring and Module-Theoretic Properties, Matrix and Gröbner Methods, and Applications, Algebra and Applications, 28, Springer, Cham, 2020.
  • G. Freudenburg, Algebraic Theory of Locally Nilpotent Derivations, Encyclopaedia of Mathematical Sciences, 136, Invariant Theory and Algebraic Transformation Groups, VII, Springer-Verlag, Berlin, 2006.
  • C. Gallego and O. Lezama, Gröbner bases for ideals of $\sigma$-PBW extensions, Comm. Algebra, 39(1) (2011), 50-75.
  • A. V. Golovashkin and V. M. Maksimov, On algebras of skew polynomials generated by quadratic homogeneous relations, J. Math. Sci. (N.Y.), 129(2) (2005), 3757-3771.
  • K. R. Goodearl and R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Second edition, London Mathematical Society Student Texts, 61, Cambridge University Press, Cambridge, 2004.
  • P. Grzeszczuk, Goldie dimension of differential operator rings, Comm. Algebra, 16(4) (1988), 689-701.
  • E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar., 107(3) (2005), 207-224.
  • S. Higuera and A. Reyes, Attached prime ideals over skew Ore polynomials, Comm. Algebra, (2024), https://doi.org/10.1080/00927872.2024.2400578.
  • D. A. Jordan, The graded algebra generated by two Eulerian derivatives, Algebr. Represent. Theory, 4(3) (2001), 249-275.
  • T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, 131, Springer-Verlag, New York, 1991.
  • T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, Springer-Verlag, New York, 1999.
  • A. Leroy and J. Matczuk, On induced modules over Ore extensions, Comm. Algebra, 32(7) (2004), 2743-2766.
  • A. Leroy and J. Matczuk, Goldie conditions for Ore extensions over semiprime rings, Algebr. Represent. Theory, 8(5) (2005), 679-688.
  • S. A. Lopes, Noncommutative algebra and representation theory: symmetry, structure & invariants, Commun. Math., 32(3) (2024), 63-117.
  • V. M. Maksimov, On a generalization of the ring of skew Ore polynomials, Russian Math. Surveys, 55(4) (2000), 817-818.
  • J. Matczuk, Goldie rank of Ore extensions, Comm. Algebra, 23(4) (1995), 1455-1471.
  • A. Nino, M. C. Ramirez and A. Reyes, A first approach to the Burchnall-Chaundy theory for quadratic algebras having PBW bases, (2024), arXiv:2401.10023v1 [math.RA].
  • A. Nino and A. Reyes, On centralizers and pseudo-multidegree functions for non-commutative rings having PBW bases, J. Algebra Appl., (2025), 2550109 (21 pp).
  • O. Ore, Linear equations in non-commutative fields, Ann. of Math. (2), 32(3) (1931), 463-477.
  • O. Ore, Theory of non-commutative polynomials, Ann. of Math. (2), 34(3) (1933), 480-508.
  • D. Quinn, Embeddings of differential operator rings and Goldie dimension, Proc. Amer. Math. Soc., 102(1) (1988), 9-16.
  • M. C. Ramirez and A. Reyes, A view toward homomorphisms and cv-polynomials between double Ore extensions, (2024), arXiv:2401.14162v1 [math.RA].
  • B. Sarath and K. Varadarajan, Dual Goldie dimension II, Comm. Algebra, 7(17) (1979), 1885-1899.
  • R. C. Shock, Polynomial rings over finite dimensional rings, Pacific J. Math., 42(1) (1972), 251-257.
  • T. H. M. Smits, Skew polynomial rings, Indag. Math. (N.S.), 30(1) (1968), 209-224.
  • K. Varadarajan, Dual Goldie dimension, Comm. Algebra, 7(6) (1979), 565-610.
  • J. J. Zhang and J. Zhang, Double Ore extensions, J. Pure Appl. Algebra, 212(12) (2008), 2668-2690.
  • J. J. Zhang and J. Zhang, Double extension regular algebras of type (14641), J. Algebra, 322(2) (2009), 373-409.

Uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials

Year 2025, Early Access, 1 - 16

Sebastian Higuera Armando Reyes

https://doi.org/10.24330/ieja.1629334

Abstract

In this paper, we study the uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials.

Keywords

Uniform dimension couniform dimension inverse polynomial module skew polynomial ring skew Ore polynomial right perfect ring Bass module

References

  • S. A. Annin, Associated and Attached Primes over Noncommutative Rings, Ph.D. Thesis, University of California, Berkeley, 2002.
  • S. A. Annin, Associated primes over Ore extension rings, J. Algebra Appl., 3(2) (2004), 193-205.
  • S. A. Annin, Couniform dimension over skew polynomial rings, Comm. Algebra, 33(4) (2005), 1195-1204.
  • S. A. Annin, Attached primes under skew polynomial extensions, J. Algebra Appl., 10(3) (2011), 537-547.
  • A. D. Bell and K. R. Goodearl, Uniform rank over differential operator rings and Poincare-Birkhoff-Witt extensions, Pacific J. Math., 131(1) (1988), 13-37.
  • P. A. A. B. Carvalho, S. A. Lopes and J. Matczuk, Double Ore extensions versus iterated Ore extensions, Comm. Algebra, 39(8) (2011), 2838-2848.
  • A. Chacon and A. Reyes, On the schematicness of some Ore polynomials of higher order generated by homogenous quadratic relations, J. Algebra Appl., (2025), 2550207 (19 pp).
  • P. M. Cohn, Quadratic extensions of skew fields, Proc. London Math. Soc. (3), 11 (1961), 531-556.
  • R. Diaz and E. Pariguan, On the $q$-meromorphic Weyl algebra, Sao Paulo J. Math. Sci., 3(2) (2009), 283-298.
  • F. Dumas, Sous-corps de fractions rationnelles des corps gauches de series de Laurent, Topics in Invariant Theory, Lecture Notes in Math., Springer, Berlin, 1478 (1991), 192-214.
  • C. Faith, Rings whose modules have maximal submodules, Publ. Mat., 39(1) (1995), 201-214.
  • W. Fajardo, C. Gallego, O. Lezama, A. Reyes, H. Suarez and H. Venegas, Skew PBW Extensions: Ring and Module-Theoretic Properties, Matrix and Gröbner Methods, and Applications, Algebra and Applications, 28, Springer, Cham, 2020.
  • G. Freudenburg, Algebraic Theory of Locally Nilpotent Derivations, Encyclopaedia of Mathematical Sciences, 136, Invariant Theory and Algebraic Transformation Groups, VII, Springer-Verlag, Berlin, 2006.
  • C. Gallego and O. Lezama, Gröbner bases for ideals of $\sigma$-PBW extensions, Comm. Algebra, 39(1) (2011), 50-75.
  • A. V. Golovashkin and V. M. Maksimov, On algebras of skew polynomials generated by quadratic homogeneous relations, J. Math. Sci. (N.Y.), 129(2) (2005), 3757-3771.
  • K. R. Goodearl and R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Second edition, London Mathematical Society Student Texts, 61, Cambridge University Press, Cambridge, 2004.
  • P. Grzeszczuk, Goldie dimension of differential operator rings, Comm. Algebra, 16(4) (1988), 689-701.
  • E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar., 107(3) (2005), 207-224.
  • S. Higuera and A. Reyes, Attached prime ideals over skew Ore polynomials, Comm. Algebra, (2024), https://doi.org/10.1080/00927872.2024.2400578.
  • D. A. Jordan, The graded algebra generated by two Eulerian derivatives, Algebr. Represent. Theory, 4(3) (2001), 249-275.
  • T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, 131, Springer-Verlag, New York, 1991.
  • T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, Springer-Verlag, New York, 1999.
  • A. Leroy and J. Matczuk, On induced modules over Ore extensions, Comm. Algebra, 32(7) (2004), 2743-2766.
  • A. Leroy and J. Matczuk, Goldie conditions for Ore extensions over semiprime rings, Algebr. Represent. Theory, 8(5) (2005), 679-688.
  • S. A. Lopes, Noncommutative algebra and representation theory: symmetry, structure & invariants, Commun. Math., 32(3) (2024), 63-117.
  • V. M. Maksimov, On a generalization of the ring of skew Ore polynomials, Russian Math. Surveys, 55(4) (2000), 817-818.
  • J. Matczuk, Goldie rank of Ore extensions, Comm. Algebra, 23(4) (1995), 1455-1471.
  • A. Nino, M. C. Ramirez and A. Reyes, A first approach to the Burchnall-Chaundy theory for quadratic algebras having PBW bases, (2024), arXiv:2401.10023v1 [math.RA].
  • A. Nino and A. Reyes, On centralizers and pseudo-multidegree functions for non-commutative rings having PBW bases, J. Algebra Appl., (2025), 2550109 (21 pp).
  • O. Ore, Linear equations in non-commutative fields, Ann. of Math. (2), 32(3) (1931), 463-477.
  • O. Ore, Theory of non-commutative polynomials, Ann. of Math. (2), 34(3) (1933), 480-508.
  • D. Quinn, Embeddings of differential operator rings and Goldie dimension, Proc. Amer. Math. Soc., 102(1) (1988), 9-16.
  • M. C. Ramirez and A. Reyes, A view toward homomorphisms and cv-polynomials between double Ore extensions, (2024), arXiv:2401.14162v1 [math.RA].
  • B. Sarath and K. Varadarajan, Dual Goldie dimension II, Comm. Algebra, 7(17) (1979), 1885-1899.
  • R. C. Shock, Polynomial rings over finite dimensional rings, Pacific J. Math., 42(1) (1972), 251-257.
  • T. H. M. Smits, Skew polynomial rings, Indag. Math. (N.S.), 30(1) (1968), 209-224.
  • K. Varadarajan, Dual Goldie dimension, Comm. Algebra, 7(6) (1979), 565-610.
  • J. J. Zhang and J. Zhang, Double Ore extensions, J. Pure Appl. Algebra, 212(12) (2008), 2668-2690.
  • J. J. Zhang and J. Zhang, Double extension regular algebras of type (14641), J. Algebra, 322(2) (2009), 373-409.
There are 39 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Articles
Authors

Sebastian Higuera This is me

Armando Reyes This is me

Early Pub Date January 29, 2025
Publication Date
Submission Date August 1, 2024
Acceptance Date December 31, 2024
Published in Issue Year 2025 Early Access

Cite

APA Higuera, S., & Reyes, A. (2025). Uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials. International Electronic Journal of Algebra1-16. https://doi.org/10.24330/ieja.1629334
AMA Higuera S, Reyes A. Uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials. IEJA. Published online January 1, 2025:1-16. doi:10.24330/ieja.1629334
Chicago Higuera, Sebastian, and Armando Reyes. “Uniform and Couniform Dimensions of Inverse Polynomial Modules over Skew Ore Polynomials”. International Electronic Journal of Algebra, January (January 2025), 1-16. https://doi.org/10.24330/ieja.1629334.
EndNote Higuera S, Reyes A (January 1, 2025) Uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials. International Electronic Journal of Algebra 1–16.
IEEE S. Higuera and A. Reyes, “Uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials”, IEJA, pp. 1–16, January 2025, doi: 10.24330/ieja.1629334.
ISNAD Higuera, Sebastian - Reyes, Armando. “Uniform and Couniform Dimensions of Inverse Polynomial Modules over Skew Ore Polynomials”. International Electronic Journal of Algebra. January 2025. 1-16. https://doi.org/10.24330/ieja.1629334.
JAMA Higuera S, Reyes A. Uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials. IEJA. 2025;:1–16.
MLA Higuera, Sebastian and Armando Reyes. “Uniform and Couniform Dimensions of Inverse Polynomial Modules over Skew Ore Polynomials”. International Electronic Journal of Algebra, 2025, pp. 1-16, doi:10.24330/ieja.1629334.
Vancouver Higuera S, Reyes A. Uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials. IEJA. 2025:1-16.