Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
The reversible property of rings was introduced by Cohn and has important generalizations in noncommutative ring theory. In this paper, reversibility of rings is investigated in relation with quasinilpotents and idempotents, and our argument is spread out based on this. We call a ring R Qnil e-reversible if for any a , b ∈ R {a,b\in R} , being a b = 0 {ab=0} implies b a e ∈ R qnil {bae\in R^{\rm qnil}} for a prescribed idempotent e ∈ R {e\in R} , where R qnil {R^{\rm qnil}} denotes the set of all quasinilpotent elements of R. In the first, we determine the set R qnil {R^{\rm qnil}} for some classes of rings to investigate the structure of Qnil e-reversible rings. In the second, we use R qnil {R^{\rm qnil}} to define Qnil e-reversibility of rings. The notion of Qnil e-reversible ring is a proper generalization of that of e-semicommutative ring, Qnil-semicommutative ring, e-reversible ring and right (left) quasi-duo ring. We obtain some relations between a ring and its quotient rings in terms of Qnil e-reversibility. Applications via some ring extensions and examples illustrating our results are provided.
The reversible property of rings was introduced by Cohn and has important generalizations in noncommutative ring theory. In this paper, reversibility of rings is investigated in relation with quasinilpotents and idempotents, and our argument is spread out based on this. We call a ring R Qnil e-reversible if for any a , b ∈ R {a,b\in R} , being a b = 0 {ab=0} implies b a e ∈ R qnil {bae\in R^{\rm qnil}} for a prescribed idempotent e ∈ R {e\in R} , where R qnil {R^{\rm qnil}} denotes the set of all quasinilpotent elements of R. In the first, we determine the set R qnil {R^{\rm qnil}} for some classes of rings to investigate the structure of Qnil e-reversible rings. In the second, we use R qnil {R^{\rm qnil}} to define Qnil e-reversibility of rings. The notion of Qnil e-reversible ring is a proper generalization of that of e-semicommutative ring, Qnil-semicommutative ring, e-reversible ring and right (left) quasi-duo ring. We obtain some relations between a ring and its quotient rings in terms of Qnil e-reversibility. Applications via some ring extensions and examples illustrating our results are provided.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.