Characterizations of lifting modules in terms of cojective modules and the class of B(M, X)

Nil Orhan; Derya Keskin Tütüncü

doi:10.1142/S0129167X05003041

Characterizations of lifting modules in terms of cojective modules and the class of B(M, X)

Nil Orhan
, Derya Keskin Tütüncü

Cebir ve Sayılar Teorisi Anabilim Dalı

Hacettepe University

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

4 Alıntılar (Scopus)

Özet

In this note, we introduce the (small, pseudo-)B(M, X)-cojective modules and we generalize (small, pseudo-)cojective modules via the class B(M, X). Let M = M₁ ⊕ M₂ be an X-amply supplemented module with the finite internal exchange property. Then for every decomposition of M = M_i ⊕ M_j, M_i is B(M_j, X)-cojective for i ≠ j, M₁ and M₂ are X-lifting if and only if M is X-lifting. We also prove that for an X-amply supplemented module M = M₁ ⊖ M₂ such that M₁ and M ₂ are indecomposable X-lifting modules, if M₂ is B(M ₁, X)-cojective and M₁ is small-B(M₂, X)-cojective then M is X-lifting.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	647-660
Sayfa sayısı	14
Dergi	International Journal of Mathematics
Hacim	16
Basın numarası	6
DOI'lar	https://doi.org/10.1142/S0129167X05003041
Yayın durumu	Yayınlandı - Tem 2005

Belgeye Erişim

10.1142/S0129167X05003041

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Bundan alıntı yap

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title = "Characterizations of lifting modules in terms of cojective modules and the class of B(M, X)",

abstract = "In this note, we introduce the (small, pseudo-)B(M, X)-cojective modules and we generalize (small, pseudo-)cojective modules via the class B(M, X). Let M = M1 ⊕ M2 be an X-amply supplemented module with the finite internal exchange property. Then for every decomposition of M = Mi ⊕ Mj, Mi is B(Mj, X)-cojective for i ≠ j, M1 and M2 are X-lifting if and only if M is X-lifting. We also prove that for an X-amply supplemented module M = M1 ⊖ M2 such that M1 and M 2 are indecomposable X-lifting modules, if M2 is B(M 1, X)-cojective and M1 is small-B(M2, X)-cojective then M is X-lifting.",

keywords = "B(m, x)-cojective module, X-lifting module",

author = "Nil Orhan and T{\"u}t{\"u}nc{\"u}, \{Derya Keskin\}",

year = "2005",

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doi = "10.1142/S0129167X05003041",

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TY - JOUR

T1 - Characterizations of lifting modules in terms of cojective modules and the class of B(M, X)

AU - Orhan, Nil

AU - Tütüncü, Derya Keskin

PY - 2005/7

Y1 - 2005/7

N2 - In this note, we introduce the (small, pseudo-)B(M, X)-cojective modules and we generalize (small, pseudo-)cojective modules via the class B(M, X). Let M = M1 ⊕ M2 be an X-amply supplemented module with the finite internal exchange property. Then for every decomposition of M = Mi ⊕ Mj, Mi is B(Mj, X)-cojective for i ≠ j, M1 and M2 are X-lifting if and only if M is X-lifting. We also prove that for an X-amply supplemented module M = M1 ⊖ M2 such that M1 and M 2 are indecomposable X-lifting modules, if M2 is B(M 1, X)-cojective and M1 is small-B(M2, X)-cojective then M is X-lifting.

AB - In this note, we introduce the (small, pseudo-)B(M, X)-cojective modules and we generalize (small, pseudo-)cojective modules via the class B(M, X). Let M = M1 ⊕ M2 be an X-amply supplemented module with the finite internal exchange property. Then for every decomposition of M = Mi ⊕ Mj, Mi is B(Mj, X)-cojective for i ≠ j, M1 and M2 are X-lifting if and only if M is X-lifting. We also prove that for an X-amply supplemented module M = M1 ⊖ M2 such that M1 and M 2 are indecomposable X-lifting modules, if M2 is B(M 1, X)-cojective and M1 is small-B(M2, X)-cojective then M is X-lifting.

KW - B(m, x)-cojective module

KW - X-lifting module

UR - https://www.scopus.com/pages/publications/21644480856

U2 - 10.1142/S0129167X05003041

DO - 10.1142/S0129167X05003041

M3 - Article

AN - SCOPUS:21644480856

SN - 0129-167X

VL - 16

SP - 647

EP - 660

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 6

ER -

Characterizations of lifting modules in terms of cojective modules and the class of B(M, X)

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