Weak π-Rickart rings

Abstract

This paper introduces and studies the weak pi-Rickart ring property, which represents a new extension of the Rickart ring condition. Regularity, extending and prime-like conditions for the weak pi-Rickart rings are defined and shows the implications between these conditions and their links with Rickart, p.q.-Baer, regular and biregular conditions. We include applications to polynomial and formal power series extensions and to triangular matrix rings, with examples given to demonstrate the results.