Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, , 1 - 19, 09.01.2024
https://doi.org/10.24330/ieja.1404416

Öz

Kaynakça

  • Y. Al-Shania  and P. F. Smith, Comultiplication modules over commutative rings, J. Commut. Algebra, 3(1) (2011), 1-29.
  • 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, London Math. Soc. Stud. Texts, 65, Cambridge University Press, Cambridge, 2006.
  • A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75 (2007), 417-429.
  • A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals in commutative rings, Bull. Korean Math. Soc., 51 (2014), 1163-1173.
  • A. Badawi, U. Tekir and E. Yetkin, On weakly 2-absorbing primary ideals of commutative rings, J. Korean Math. Soc., 52 (2015), 97-111.
  • S. Ebrahimi Atani, On pure-injective modules over pullback rings, Comm. Algebra, 28 (2000), 4037-4069.
  • S. Ebrahimi Atani, On secondary modules over Dedekind domains, Southeast Asian Bull. Math, 25 (2001), 1-6.
  • S. Ebrahimi Atani, On secondary modules over pullback rings, Comm. Algebra, 30 (2002), 2675-2685.
  • S. Ebrahimi Atani, Indecomposable weak multiplication modules over Dedekind domains, Demonstratio Math., 41 (2008), 33-43.
  • S. Ebrahimi Atani and F. Farzalipour, Weak multiplication modules over a pullback of Dedekind domains, Colloq. Math., 114 (2009), 99-112.
  • S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel and M. Sedghi Shanbeh Bazari, Pseudo-absorbing multiplication modules over a pullback ring, J. Pure Appl. Algebra, 222 (2018), 3124-3136.
  • A. Facchini and P. Vamos, Injective modules over pullbacks, J. London Math. Soc. (2), 31 (1985), 425-438.
  • J. Haefner and L. Klingler, Special quasi-triads and integral group rings of finite representation type I, J. Algebra, 158 (1993), 279-322.
  • J. Haefner and L. Klingler, Special quasi-triads and integral group rings of finite representation type II, J. Algebra, 158 (1993), 323-374.
  • I. Kaplansky, Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc., 72 (1952), 327-340.
  • L. Klingler, Integral representations of groups of square-free order, J. Algebra, 129 (1990), 26-74.
  • P. A. Krylov and A. A. Tuganbaev, Modules over Discrete Valuation Rings, De Gruyter Expositions in Mathematics, Berlin, 2018.
  • L. S. Levy, Modules over pullbacks and subdirect sums, J. Algebra, 71 (1981), 50-61.
  • 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 Dedekind-like rings, J. Algebra, 93 (1985), 1-116.
  • R. L. McCasland, M. E. Moore and P. F. Smith, On the spectrum of a module over a commutative ring, Comm. Algebra, 25 (1997), 79-103.
  • M. E. Moore and S. J. Smith, Prime and radical submodules of modules over commutative rings, Comm. Algebra, 30 (2002), 5037-5064.
  • 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. Akad. Nauk SSSR Ser. Mat., 33 (1969), 65-89.
  • Sh. Payrovi and S. Babaei, On 2-absorbing submodules, Algebra Colloq., 19(1) (2012), 913-920.
  • M. Prest, Model Theory and Modules, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1988.
  • M. Prest, Ziegler spectra of tame hereditary algebras, J. Algebra, 207 (1998), 146-164.
  • C. M. Ringel, Some algebraically compact modules I, Abelian Groups and Modules, Math. Appl., vol. 343, Padova, 1994, Kluwer Acad. Publ., Dordrecht (1995), 419-439.
  • C. M. Ringel, The Ziegler spectrum of a tame hereditary algebra, Colloq. Math., 76 (1998), 105-115.
  • D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl., Gordon and Breach Science Publishers, Montreux, 1992.
  • Y. Wang and Y. Liu, A note on comultiplication modules, Algebra Colloq., 21(1) (2014), 147-150.
  • R. B.Warfield, Purity and algebraic compactness for modules, Pacific J. Math., 28 (1969), 699-719.

Pseudo-absorbing comultiplication modules over a pullback ring

Yıl 2024, , 1 - 19, 09.01.2024
https://doi.org/10.24330/ieja.1404416

Öz

In this paper, we introduce the notion of pseudo-absorbing
comultiplication modules. A full description of all indecomposable pseudo-absorbing
comultiplication modules with finite dimensional top over certain kinds of pullback rings
are given and establish a connection between the pseudo-absorbing comultiplication
modules and the pure-injective modules over such rings.

Kaynakça

  • Y. Al-Shania  and P. F. Smith, Comultiplication modules over commutative rings, J. Commut. Algebra, 3(1) (2011), 1-29.
  • 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, London Math. Soc. Stud. Texts, 65, Cambridge University Press, Cambridge, 2006.
  • A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75 (2007), 417-429.
  • A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals in commutative rings, Bull. Korean Math. Soc., 51 (2014), 1163-1173.
  • A. Badawi, U. Tekir and E. Yetkin, On weakly 2-absorbing primary ideals of commutative rings, J. Korean Math. Soc., 52 (2015), 97-111.
  • S. Ebrahimi Atani, On pure-injective modules over pullback rings, Comm. Algebra, 28 (2000), 4037-4069.
  • S. Ebrahimi Atani, On secondary modules over Dedekind domains, Southeast Asian Bull. Math, 25 (2001), 1-6.
  • S. Ebrahimi Atani, On secondary modules over pullback rings, Comm. Algebra, 30 (2002), 2675-2685.
  • S. Ebrahimi Atani, Indecomposable weak multiplication modules over Dedekind domains, Demonstratio Math., 41 (2008), 33-43.
  • S. Ebrahimi Atani and F. Farzalipour, Weak multiplication modules over a pullback of Dedekind domains, Colloq. Math., 114 (2009), 99-112.
  • S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel and M. Sedghi Shanbeh Bazari, Pseudo-absorbing multiplication modules over a pullback ring, J. Pure Appl. Algebra, 222 (2018), 3124-3136.
  • A. Facchini and P. Vamos, Injective modules over pullbacks, J. London Math. Soc. (2), 31 (1985), 425-438.
  • J. Haefner and L. Klingler, Special quasi-triads and integral group rings of finite representation type I, J. Algebra, 158 (1993), 279-322.
  • J. Haefner and L. Klingler, Special quasi-triads and integral group rings of finite representation type II, J. Algebra, 158 (1993), 323-374.
  • I. Kaplansky, Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc., 72 (1952), 327-340.
  • L. Klingler, Integral representations of groups of square-free order, J. Algebra, 129 (1990), 26-74.
  • P. A. Krylov and A. A. Tuganbaev, Modules over Discrete Valuation Rings, De Gruyter Expositions in Mathematics, Berlin, 2018.
  • L. S. Levy, Modules over pullbacks and subdirect sums, J. Algebra, 71 (1981), 50-61.
  • 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 Dedekind-like rings, J. Algebra, 93 (1985), 1-116.
  • R. L. McCasland, M. E. Moore and P. F. Smith, On the spectrum of a module over a commutative ring, Comm. Algebra, 25 (1997), 79-103.
  • M. E. Moore and S. J. Smith, Prime and radical submodules of modules over commutative rings, Comm. Algebra, 30 (2002), 5037-5064.
  • 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. Akad. Nauk SSSR Ser. Mat., 33 (1969), 65-89.
  • Sh. Payrovi and S. Babaei, On 2-absorbing submodules, Algebra Colloq., 19(1) (2012), 913-920.
  • M. Prest, Model Theory and Modules, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1988.
  • M. Prest, Ziegler spectra of tame hereditary algebras, J. Algebra, 207 (1998), 146-164.
  • C. M. Ringel, Some algebraically compact modules I, Abelian Groups and Modules, Math. Appl., vol. 343, Padova, 1994, Kluwer Acad. Publ., Dordrecht (1995), 419-439.
  • C. M. Ringel, The Ziegler spectrum of a tame hereditary algebra, Colloq. Math., 76 (1998), 105-115.
  • D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl., Gordon and Breach Science Publishers, Montreux, 1992.
  • Y. Wang and Y. Liu, A note on comultiplication modules, Algebra Colloq., 21(1) (2014), 147-150.
  • R. B.Warfield, Purity and algebraic compactness for modules, Pacific J. Math., 28 (1969), 699-719.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Makaleler
Yazarlar

Shahabaddin Ebrahimi Atanı

Mehdi Khoramdel

Saboura Dolatı Pıshhesarı

Erken Görünüm Tarihi 22 Aralık 2023
Yayımlanma Tarihi 9 Ocak 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

APA Atanı, S. E., Khoramdel, M., & Dolatı Pıshhesarı, S. (2024). Pseudo-absorbing comultiplication modules over a pullback ring. International Electronic Journal of Algebra, 35(35), 1-19. https://doi.org/10.24330/ieja.1404416
AMA Atanı SE, Khoramdel M, Dolatı Pıshhesarı S. Pseudo-absorbing comultiplication modules over a pullback ring. IEJA. Ocak 2024;35(35):1-19. doi:10.24330/ieja.1404416
Chicago Atanı, Shahabaddin Ebrahimi, Mehdi Khoramdel, ve Saboura Dolatı Pıshhesarı. “Pseudo-Absorbing Comultiplication Modules over a Pullback Ring”. International Electronic Journal of Algebra 35, sy. 35 (Ocak 2024): 1-19. https://doi.org/10.24330/ieja.1404416.
EndNote Atanı SE, Khoramdel M, Dolatı Pıshhesarı S (01 Ocak 2024) Pseudo-absorbing comultiplication modules over a pullback ring. International Electronic Journal of Algebra 35 35 1–19.
IEEE S. E. Atanı, M. Khoramdel, ve S. Dolatı Pıshhesarı, “Pseudo-absorbing comultiplication modules over a pullback ring”, IEJA, c. 35, sy. 35, ss. 1–19, 2024, doi: 10.24330/ieja.1404416.
ISNAD Atanı, Shahabaddin Ebrahimi vd. “Pseudo-Absorbing Comultiplication Modules over a Pullback Ring”. International Electronic Journal of Algebra 35/35 (Ocak 2024), 1-19. https://doi.org/10.24330/ieja.1404416.
JAMA Atanı SE, Khoramdel M, Dolatı Pıshhesarı S. Pseudo-absorbing comultiplication modules over a pullback ring. IEJA. 2024;35:1–19.
MLA Atanı, Shahabaddin Ebrahimi vd. “Pseudo-Absorbing Comultiplication Modules over a Pullback Ring”. International Electronic Journal of Algebra, c. 35, sy. 35, 2024, ss. 1-19, doi:10.24330/ieja.1404416.
Vancouver Atanı SE, Khoramdel M, Dolatı Pıshhesarı S. Pseudo-absorbing comultiplication modules over a pullback ring. IEJA. 2024;35(35):1-19.