In this paper we study modules with the W F I<sup>+</sup>-extending property. We prove that if M satisfies the W F I<sup>+</sup>-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then M decompose into ...
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https://www.riss.kr/link?id=A107811143
2021
English
SCOPUS,KCI등재,ESCI
학술저널
239-248(10쪽)
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
In this paper we study modules with the W F I<sup>+</sup>-extending property. We prove that if M satisfies the W F I<sup>+</sup>-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then M decompose into ...
In this paper we study modules with the W F I<sup>+</sup>-extending property. We prove that if M satisfies the W F I<sup>+</sup>-extending, pseudo duo properties and M/(Soc M) has finite uniform dimension then M decompose into a direct sum of a semisimple submodule and a submodule of finite uniform dimension. In particular, if M satisfies the W F I<sup>+</sup>-extending, pseudo duo properties and ascending chain (respectively, descending chain) condition on essential submodules then M = M<sub>1</sub> ⊕ M<sub>2</sub> for some semisimple submodule M<sub>1</sub> and Noetherian (respectively, Artinian) submodule M<sub>2</sub>. Moreover, we show that if M is a W F I-extending module with pseudo duo, C<sub>2</sub> and essential socle then the quotient ring of its endomorphism ring with Jacobson radical is a (von Neumann) regular ring. We provide several examples which illustrate our results.
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