Lifting Modules Over Right Perfect Rings

Kuratomi, Yosuke; Chang, Chaehoon

doi:10.1080/00927870701405132

Cited by 10 publications

(3 citation statements)

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“…Hence R = Soc(R R ). Lemma 2.3 (cf., [4] and [8]). A ring R is right perfect (semiperfect) if and only if every (finitely generated) projective right R-module is lifting.…”

Section: Preliminariesmentioning

confidence: 98%

Finitely Generated Modules over Semilocal Rings and Characterizations of (Semi-)Perfect Rings

Chang¹

2008

Kyungpook mathematical journal

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Lomp [9] has studied finitely generated projective modules over semilocal rings. He obtained the following: finitely generated projective modules over semilocal rings are semilocal. We shall give necessary and sufficient conditions for finitely generated modules to be semilocal modules. By using a lifting property, we also give characterizations of right perfect (semiperfect) rings. Our main results can be summarized as follows: (1) Let M be a finitely generated module. Then M has finite hollow dimension if and only if M is weakly supplemented if and only if M is semilocal. (2) A ring R is right perfect if and only if every flat right R-module is lifting and every right R-module has a flat cover if and only if every quasi-projective right R-module is lifting. (3) A ring R is semiperfect if and only if every finitely generated flat right R-module is lifting if and only if RR satisfies the lifting property for simple factor modules.

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“…Hence R = Soc(R R ). Lemma 2.3 (cf., [4] and [8]). A ring R is right perfect (semiperfect) if and only if every (finitely generated) projective right R-module is lifting.…”

Section: Preliminariesmentioning

confidence: 98%

Finitely Generated Modules over Semilocal Rings and Characterizations of (Semi-)Perfect Rings

Chang¹

2008

Kyungpook mathematical journal

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“…Since R is generalized uniserial, R is right perfect. Then there exists a direct sum decomposition M = ⊕ I M i , where M i is hollow by [7,Theorem 3.4]. Furthermore, M is extending.…”

Section: Theorem 32 Every Local Summand Of An Extending Lifting Modmentioning

confidence: 99%

“…Recently Chang showed that if every co-closed submodule of any projective module P contains Rad(P ), then every X-lifting module over a right perfect ring has an indecomposable decomposition (cf. [1,3,7,12]). …”

Section: Introductionmentioning

confidence: 99%

On the Decomposition of Extending Lifting Modules

Chang¹,

Shin²

2009

Bulletin of the Korean Mathematical Society

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Abstract. In 1984, Oshiro [11] has studied the decomposition of continuous lifting modules. He obtained the following: every continuous lifting module has an indecomposable decomposition. In this paper, we study extending lifting modules. We show that every extending lifting module has an indecomposable decomposition. This result is an expansion of Oshiro's result mentioned above. And we consider some application of this result.

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