Weak π-Rickart rings

KARA ŞEN Y.

Communications in Algebra, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1080/00927872.2025.2451085
  • Journal Name: Communications in Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Baer ring, generalized upper triangular matrix ring, polynomial extensions, Rickart ring
  • Bursa Uludag University Affiliated: Yes

Abstract

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