*-Rickart Property for Rings with Involution-Reference-Cited by-同舟云学术

*-Rickart Property for Rings with Involution

Published:2024-06-17 Issue:1 Volume:30_NS4 Page:80-90
ISSN:0865-2090
Container-title:Mathematica Pannonica
language:
Short-container-title:MathPann

Author:

Tajuddin Muhammad T.¹,Aburawash Usama A.¹,Saad Muhammad¹

Affiliation:

1. Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21568, Egypt

Abstract

This paper introduces and examines the concept of a *-Rickart *-ring, and proves that every Rickart *-ring is also a *-Rickart *-ring. A necessary and sufficient condition for a *-Rickart *-ring to be a Rickart *-ring is also provided. The relationship between *-Rickart *-rings and *-Baer *-rings is investigated, and several properties of *-Rickart *-rings are presented. The paper demonstrates that the property of *-Rickart extends to both the center and *-corners of a *-ring, and investigates the extension of a *-Rickart *-ring to its polynomial *-ring. Additionally, *-Rickart *-rings with descending chain condition on *-biideals are studied, and all *-Rickart (*-Baer) *-rings with finitely many elements are classified.

Publisher

Akademiai Kiado Zrt.

Link

https://akjournals.com/downloadpdf/journals/314/30_NS4/1/article-p80.xml

Reference22 articles.

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5. [5]Aburawash, U. A., and Saad, M. *-Baer property for rings with involution. Stud. Sci. Math. Hung. 53, 2 (2016), 243-255.