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http://dx.doi.org/10.5666/KMJ.2021.61.2.239

Weak F I-extending Modules with ACC or DCC on Essential Submodules  

Tercan, Adnan (Department of Mathematics, Hacettepe University, Beytepe Campus)
Yasar, Ramazan (Hacettepe-ASO 1.OSB Vocational School, Hacettepe University)
Publication Information
Kyungpook Mathematical Journal / v.61, no.2, 2021 , pp. 239-248 More about this Journal
Abstract
In this paper we study modules with the W F I+-extending property. We prove that if M satisfies the W F I+-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+-extending, pseudo duo properties and ascending chain (respectively, descending chain) condition on essential submodules then M = M1 ⊕ M2 for some semisimple submodule M1 and Noetherian (respectively, Artinian) submodule M2. Moreover, we show that if M is a W F I-extending module with pseudo duo, C2 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.
Keywords
CS-module; uniform dimension; ascending chain condition on essential submodules; F I-extending; W F I-extending;
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