End-regularity of zero-divisor graphs of group rings

Abstract

ABSTRACTA graph Γ is said to be End-regular if its endomorphism monoid End(Γ) is regular. D. Lu and T. Wu [25] posed an open problem: Given a ring R, when does the zero-divisor graph Γ(R) have a regular endomorphism monoid? and they solved the problem for R a commutative ring with at least one nontrivial idempotent. In this paper, we solve this problem for zero-divisor graphs of group rings.