Abstract
The paper studies the following question: Given a ring R , when does the zero-divisor graph Γ ( R ) have a regular endomorphism monoid? We prove if R contains at least one nontrivial idempotent, then Γ ( R ) has a regular endomorphism monoid if and only if R is isomorphic to one of the following rings: Z 2 × Z 2 × Z 2 ; Z 2 × Z 4 ; Z 2 × ( Z 2 [ x ] / ( x 2 ) ) ; F 1 × F 2 , where F 1 , F 2 are fields. In addition, we determine all positive integers n for which Γ ( Z n ) has the property.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
