Roohallah Daneshpayeh, Sirus Jahanpanah

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Every classical algebra is a set equipped with binary operations that operate under certain axiom principles. The generalization of classical algebras to hyperalgebras has been created with the aim of generalizing operations to hyperoperations that apply to specific subject principles. This paper introduces the concept of reproduced general hyperrings as a generalization of rings and investigates and analyzes some of their essential properties. This study defines the notation of reproduced hyperideals in reproduced general hyperrings, consider the ideals of finite rings and obtain the finite and cyclic hyperideals. In the endl, we introduce and show that a principal Ideal domain finite reproduced general hyperring is Ideal-absorbing.


hyperring, principal ideal domain, axioms

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