Abstract
This paper introduces and studies the weak π -Rickart ring property, which represents a new extension of the Rickart ring condition. Regularity, extending and prime-like conditions for the weak π -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.
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