Characterizing wsr1 Condition by Completions of Diagrams

Abstract:

      We prove that for a right quasi-projective R-module M, End_R (M) satisfies wsr1 condition if and only if M is a T-projective module. We prove that wsr1 condition is left-right symmetric. For von Neumann regular ring R, R satisfies wsr1 if and only if R is one-sided unit regular.