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

Division of Algebra and Number Theory

Hacettepe University

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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 = 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.

Original language	English
Pages (from-to)	647-660
Number of pages	14
Journal	International Journal of Mathematics
Volume	16
Issue number	6
DOIs	https://doi.org/10.1142/S0129167X05003041
Publication status	Published - Jul 2005

Keywords

B(m, x)-cojective module
X-lifting module

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10.1142/S0129167X05003041

Cite this

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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.",

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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

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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

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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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Keywords

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