On τ_M-Semilocal Modules and Rings - Talebi, Y.; Amoozegar, T.; Mansoury, Zh. (Communications in Mathematics and Applications, 2010)
Let τ_M be any preradical for σ[M] and N any module in σ[M]. In [2], Al-Takhman, Lomp and Wisbauer defined and studied the concept of τ_M-supplemented module. In this paper we define the concept of weakly τ_M-supplemented module and investigate some properties of such modules. We show that weakly τ_M-supplemented module N is τ_M-semilocal (i.e., N/τ_M(N) is semisimple) and that R is a τ-semilocal ring if and only if _RR (or R_R) is weakly τ_M-supplemented.