Zero Divisor Graphs Based on General Hyperrings‎

Abstract

This paper introduces the concepts of reproduced general hyperring and valued-orderable general hyperring and investigates some properties of these classes of general hyperrings‎. ‎It presents the notions of‎ ‎zero divisors and zero divisor graphs are founded on the absorbing elements of general hyperrings‎. ‎General hyperrings can have more than one zeroing element‎, ‎and therefore‎, ‎based on the zeroing elements‎, ‎multiple zero divisors can be obtained‎. ‎In this study‎, ‎we discuss the isomorphism of zero divisor graphs based on the diversity of divisors of zero divisors‎. ‎The non-empty intersection of the set of absorbing elements and the hyperproduct of zero divisors of general hyperrings play a major role in the production of zero divisor graphs‎. ‎Indeed it investigated a type classification of zero divisor graphs based on the finite general hyperrings‎. ‎We discuss the finite reproduced general hyperrings‎, ‎investigate their zero divisor graphs‎, ‎and show that an infinite reproduced general hyperring can have a finite zero divisor graph‎.