Regular elements determined by generalized inverses

2018/06/26 by Alahmadi, Adel, Jain, S. K., Leroy, André
#16E50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1806.10212

Abstract

In a semiprime ring, von Neumann regular elements are determined by their inner inverses. In particular, for elements a,b of a von Neumann regular ring R, a=b if and only if I(a)=I(b), where I(x) denotes the set of inner inverses of x∈ R. We also prove that, in a semiprime ring, the same is true for reflexive inverses.

Related

• The one-sided inverse along two elements in rings
• The inverse along an element in rings
• Characterizations of the (b, c)-inverse in a ring
• Relative regular modules. Applications to von Neumann regular rings
• Existence criteria and expressions of the (b,c)-inverse in rings and its applications