A generalization of $${\varvec{\pi }}$$ π -regular seminear-ring

Zhaleh Shamsi (), Shaban Ghalandarzadeh () and Parastoo Malakooti-Rad ()
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Zhaleh Shamsi: Islamic Azad University
Shaban Ghalandarzadeh: K. N. Toosi University of Technology
Parastoo Malakooti-Rad: Islamic Azad University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 1, 210-218

Abstract: Abstract The aim of this paper is to introduce and investigate generalization of $$\pi $$ π -regular seminear-rings. We determine the structural property of regular constant clean, the generalization of $$\pi $$ π -regular and strongly $$\pi $$ π -regular seminear-rings. Moreover, we give a new definition of Utumi seminear-rings based on the constant elements. Then we show that such seminear-rings contain the above structure of seminear-rings despite certain conditions. Assuming that I is an ideal of a regular constant clean seminear-ring S, we prove that S/I is a quotient of seminear-rings. We find the relation between regular constant clean seminear-rings and their quotients.

Keywords: Constant element; Constant clean; Regular constant clean; Strongly regular constant clean; Weakly constant clean (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00244-7

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