Araştırma Makalesi
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ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS

Yıl 2019, , 95 - 110, 11.07.2019
https://doi.org/10.24330/ieja.586980

Öz

We classify all indecomposable quasi comultiplication modules
over pullback of two Dedekind domains. We extend the de nitions and the
results of comultiplication modules over pullback rings to a more general quasi
comultiplication modules case.

Kaynakça

  • A. Abbasi and D. Hassanzadeh-Lelekaami, Quasi-prime submodules and developed Zariski topology, Algebra Colloq., 19 (2012), 1089-1108.
  • D. M. Arnold and R. C. Laubenbacher, Finitely generated modules over pullback rings, J. Algebra, 184 (1996), 304-332.
  • I. Assem, D. Simson and A. Skowronski, Elements of the Representation Theory of Associative Algebras, Vol.1, Techniques of Representation Theory, London Mathematical Society Student Texts, 65, Cambridge University Press, Cambridge, 2006.
  • H. Bass, On the ubiquity of Gorenstein rings, Math. Z., 82 (1963), 8-28.
  • S. Ebrahimi Atani, On pure-injective modules over pullback rings, Comm. Algebra, 28 (2000), 4037-4069.
  • S. Ebrahimi Atani, On secondary modules over pullback rings, Comm. Algebra, 30 (2002), 2675-2685.
  • R. Ebrahimi Atani and S. Ebrahimi Atani, Comultiplication modules over a pullback of Dedekind domains, Czechoslovak Math. J., 59 (2009), 1103-1114.
  • R. Ebrahimi Atani and S. Ebrahimi Atani, Weak comultiplication modules over a pullback of commutative local Dedekind domains, Algebra Discrete Math., 1 (2009), 1-13.
  • R. Ebrahimi Atani and S. Ebrahimi Atani, On primarily multiplication modules over pullback rings, Algebra Discrete Math., 11 (2011), 1-17.
  • S. Ebrahimi Atani and F. Esmaeili Khalil Saraei, Indecomposable primarily comultiplication modules over a pullback of two Dedekind domains, Colloq. Math., 120 (2010), 23-42.
  • S. Ebrahimi Atani and F. Esmaeili Khalil Saraei, On P-torsion modules over a pullback of two Dedekind domains, Georgian Math. J., 19 (2012), 473-488.
  • S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel and M. Sedghi Shanbeh Bazari, Absorbing comultiplication modules over a pullback ring, Int. Electron. J. Algebra, 24 (2018), 31-49.
  • F. Esmaeili Khalil Saraei, On pseudo-prime multiplication modules over pullback rings, Colloq. Math., 143 (2016), 63-78.
  • A. Facchini, Fiber products and Morita duality for commutative rings, Rend. Sem. Mat. Univ. Padova, 67 (1982), 143-159.
  • A. Facchini and P. Vamos, Injective modules over pullbacks, J. London Math. Soc., 31 (1985), 425-438.
  • W. J. Heinzer, L. J. Ratlif, Jr. and D. E. Rush, Strongly irreducible ideals of a commutative ring, J. Pure Appl. Algebra, 166 (2002), 267-275.
  • R. Kielpinski, On Gamma-pure injective modules, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 15 (1967), 127-131.
  • V. V. Kiricenko, Classi cation of the pairs of mutually annihilating operators in a graded space and representations of a dyad of generalized uniserial algebras, In: \Rings and Linear Groups", Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 75 (1978), 91-109, 196-197.
  • L. Klingler, Integral representations of groups of square-free order, J. Algebra, 129 (1990), 26-74.
  • L. S. Levy, Mixed modules over ZG, G cyclic of prime order, and over related Dedekind pullbacks, J. Algebra, 71 (1981), 62-114.
  • L. S. Levy, Modules over pullbacks and subdirect sums, J. Algebra, 71 (1981), 50-61.
  • L. S. Levy, Modules over Dedekind-like rings, J. Algebra, 93 (1985), 1-116.
  • L. A. Nazarova and A. V. Roiter, Finitely generated modules over a dyad of two local Dedekind rings, and nite groups which possess an abelian normal divisor of index p, Izv. Acad. Nauk SSSR Ser. Mat., 33 (1969), 65-89.
  • M. Prest, Model Theory and Modules, London Mathematical Society Lecture Note Series, 130, Cambridge University Press, Cambridge, 1988.
  • D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Applications, 4, Gordon and Breach Science Publishers, Switzerland-Australia, 1992.
  • D. Simson and A. Skowronski, Elements of the Representation Theory of Associative Algebras, Representation-In nite Tilted Algebras, Vol. 3, London Mathematical Society Student Texts, 72, Cambridge University Press, Cambridge, 2007.
  • R. B. War eld, Jr., Purity and algebraic compactness for modules, Paci c J. Math., 28 (1969), 699-719.
  • A. N. Wiseman, Projective modules over pullback rings, Math. Proc. Cambridge Philos. Soc., 97 (1985), 399-406.
Yıl 2019, , 95 - 110, 11.07.2019
https://doi.org/10.24330/ieja.586980

Öz

Kaynakça

  • A. Abbasi and D. Hassanzadeh-Lelekaami, Quasi-prime submodules and developed Zariski topology, Algebra Colloq., 19 (2012), 1089-1108.
  • D. M. Arnold and R. C. Laubenbacher, Finitely generated modules over pullback rings, J. Algebra, 184 (1996), 304-332.
  • I. Assem, D. Simson and A. Skowronski, Elements of the Representation Theory of Associative Algebras, Vol.1, Techniques of Representation Theory, London Mathematical Society Student Texts, 65, Cambridge University Press, Cambridge, 2006.
  • H. Bass, On the ubiquity of Gorenstein rings, Math. Z., 82 (1963), 8-28.
  • S. Ebrahimi Atani, On pure-injective modules over pullback rings, Comm. Algebra, 28 (2000), 4037-4069.
  • S. Ebrahimi Atani, On secondary modules over pullback rings, Comm. Algebra, 30 (2002), 2675-2685.
  • R. Ebrahimi Atani and S. Ebrahimi Atani, Comultiplication modules over a pullback of Dedekind domains, Czechoslovak Math. J., 59 (2009), 1103-1114.
  • R. Ebrahimi Atani and S. Ebrahimi Atani, Weak comultiplication modules over a pullback of commutative local Dedekind domains, Algebra Discrete Math., 1 (2009), 1-13.
  • R. Ebrahimi Atani and S. Ebrahimi Atani, On primarily multiplication modules over pullback rings, Algebra Discrete Math., 11 (2011), 1-17.
  • S. Ebrahimi Atani and F. Esmaeili Khalil Saraei, Indecomposable primarily comultiplication modules over a pullback of two Dedekind domains, Colloq. Math., 120 (2010), 23-42.
  • S. Ebrahimi Atani and F. Esmaeili Khalil Saraei, On P-torsion modules over a pullback of two Dedekind domains, Georgian Math. J., 19 (2012), 473-488.
  • S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel and M. Sedghi Shanbeh Bazari, Absorbing comultiplication modules over a pullback ring, Int. Electron. J. Algebra, 24 (2018), 31-49.
  • F. Esmaeili Khalil Saraei, On pseudo-prime multiplication modules over pullback rings, Colloq. Math., 143 (2016), 63-78.
  • A. Facchini, Fiber products and Morita duality for commutative rings, Rend. Sem. Mat. Univ. Padova, 67 (1982), 143-159.
  • A. Facchini and P. Vamos, Injective modules over pullbacks, J. London Math. Soc., 31 (1985), 425-438.
  • W. J. Heinzer, L. J. Ratlif, Jr. and D. E. Rush, Strongly irreducible ideals of a commutative ring, J. Pure Appl. Algebra, 166 (2002), 267-275.
  • R. Kielpinski, On Gamma-pure injective modules, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 15 (1967), 127-131.
  • V. V. Kiricenko, Classi cation of the pairs of mutually annihilating operators in a graded space and representations of a dyad of generalized uniserial algebras, In: \Rings and Linear Groups", Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 75 (1978), 91-109, 196-197.
  • L. Klingler, Integral representations of groups of square-free order, J. Algebra, 129 (1990), 26-74.
  • L. S. Levy, Mixed modules over ZG, G cyclic of prime order, and over related Dedekind pullbacks, J. Algebra, 71 (1981), 62-114.
  • L. S. Levy, Modules over pullbacks and subdirect sums, J. Algebra, 71 (1981), 50-61.
  • L. S. Levy, Modules over Dedekind-like rings, J. Algebra, 93 (1985), 1-116.
  • L. A. Nazarova and A. V. Roiter, Finitely generated modules over a dyad of two local Dedekind rings, and nite groups which possess an abelian normal divisor of index p, Izv. Acad. Nauk SSSR Ser. Mat., 33 (1969), 65-89.
  • M. Prest, Model Theory and Modules, London Mathematical Society Lecture Note Series, 130, Cambridge University Press, Cambridge, 1988.
  • D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Applications, 4, Gordon and Breach Science Publishers, Switzerland-Australia, 1992.
  • D. Simson and A. Skowronski, Elements of the Representation Theory of Associative Algebras, Representation-In nite Tilted Algebras, Vol. 3, London Mathematical Society Student Texts, 72, Cambridge University Press, Cambridge, 2007.
  • R. B. War eld, Jr., Purity and algebraic compactness for modules, Paci c J. Math., 28 (1969), 699-719.
  • A. N. Wiseman, Projective modules over pullback rings, Math. Proc. Cambridge Philos. Soc., 97 (1985), 399-406.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

S. Ebrahimi Atani

F. Esmaeili Khalil Saraei Bu kişi benim

Yayımlanma Tarihi 11 Temmuz 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Atani, S. E., & Saraei, F. E. K. (2019). ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS. International Electronic Journal of Algebra, 26(26), 95-110. https://doi.org/10.24330/ieja.586980
AMA Atani SE, Saraei FEK. ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS. IEJA. Temmuz 2019;26(26):95-110. doi:10.24330/ieja.586980
Chicago Atani, S. Ebrahimi, ve F. Esmaeili Khalil Saraei. “ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS”. International Electronic Journal of Algebra 26, sy. 26 (Temmuz 2019): 95-110. https://doi.org/10.24330/ieja.586980.
EndNote Atani SE, Saraei FEK (01 Temmuz 2019) ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS. International Electronic Journal of Algebra 26 26 95–110.
IEEE S. E. Atani ve F. E. K. Saraei, “ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS”, IEJA, c. 26, sy. 26, ss. 95–110, 2019, doi: 10.24330/ieja.586980.
ISNAD Atani, S. Ebrahimi - Saraei, F. Esmaeili Khalil. “ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS”. International Electronic Journal of Algebra 26/26 (Temmuz 2019), 95-110. https://doi.org/10.24330/ieja.586980.
JAMA Atani SE, Saraei FEK. ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS. IEJA. 2019;26:95–110.
MLA Atani, S. Ebrahimi ve F. Esmaeili Khalil Saraei. “ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS”. International Electronic Journal of Algebra, c. 26, sy. 26, 2019, ss. 95-110, doi:10.24330/ieja.586980.
Vancouver Atani SE, Saraei FEK. ON QUASI COMULTIPLICATION MODULES OVER PULLBACK RINGS. IEJA. 2019;26(26):95-110.