On tau-discrete modules

Authors : Burcu Nişancı Türkmen, Ergül Türkmen

Pages : 37-43

Doi:10.18185/erzifbed.1251658

View : 69 | Download : 72

Publication Date : 2024-03-28

Article Type : Research Paper

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