JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.20, no.08, 2021 (Peer-Reviewed Journal)
Article / Article
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
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Right Rickart ring, right p.p ring, Baer ring, p-Baer ring, projection invariant, generalized triangular matrix ring, matrix ring, polynomial extensions, regular ring, exchange ring, Banach algebra, IDEMPOTENTS, EXTENSIONS, SETS
In this paper, we introduce and investigate three new versions of the Rickart condition for rings. These conditions, as well as, three new corresponding regularities are defined using projection invariance. We show how these conditions relate to each other as well as their connections to the well-known Baer, Rickart, quasi-Baer, p.q.-Baer, regular, and biregular conditions. Applications to polynomial extensions and to triangular and full matrix rings are provided. Examples illustrate and delimit results.