On tau-discrete modules

Year 2024, Volume: 17 Issue: 1, 37 - 43, 28.03.2024

Burcu Nişancı Türkmen , Ergül Türkmen

https://doi.org/10.18185/erzifbed.1251658

Abstract

An R-module M is said to be (quasi) τ-discrete if M is τ-lifting and has the property (D_2) (respectively, has the property (D_3)), where τ is a preradical in R-mod. It is shown that: (1) direct summands of a (quasi) τ-discrete module are (quasi) τ-discrete; (2) a projective module M is τ-discrete iff M/(τ(M)) is semisimple and τ(M) is QSL; (3) if a projective module M is Soc-lifting, then M/(Soc(M)) is Soc-discrete and Rad(M/Soc(M) ) is semisimple.

Keywords

preradical, τ-lifting mdule, (quasi) τ-discrete module.

Supporting Institution

This work was presented in 3rd International Conference on Engineering and Applied Natural Sciences (ICEANS 2023) on 14-17 January in 2023 at Konya/Turkey.

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