Zero Divisor Graphs Based on General Hyperrings‎

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Article Type:
Research/Original Article (دارای رتبه معتبر)
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.
Language:
English
Published:
Journal of Algebraic Hyperstructures and Logical Algebras, Volume:4 Issue: 2, Spring 2023
Pages:
131 to 149
https://www.magiran.com/p2663995  
سامانه نویسندگان
  • Mohammad Hamidi
    Author
    Associate Professor Mathematics- Science, Payame Noor University, Tehran, Iran
    Hamidi، Mohammad
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