$(u,v)$-ABSORBING (PRIME) HYPERIDEALS OVER COMMUTATIVE MULTIPLICATIVE HYPERRINGS

Document Type : Original Manuscript

Author

Department of Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran.

10.22044/jas.2025.15222.1899

Abstract

In this paper, we consider the class of multiplicative hyperrings and introduce an expansion of the ‎$‎v‎$‎-absorbing hyperideals called ‎$‎(u,v)‎$‎-absorbing hyperideals. ‎ ‎A proper hyperideal $Q$ of a multiplicative hyperring $A$ is called a $(u,v)$-absorbing hyperideal ‎ if $x_1 \circ \cdots \circ x_u \subseteq Q$ for non-unit elements $x_1,\cdots, x_u \in A$, then there are ‎$‎v‎$ ‎of the ‎$‎x_i^,‎$‎s whose product is a subset of ‎$‎Q‎$ where ‎$‎u,v \in ‎\mathbb{N}‎‎$ ‎with ‎‎$‎u >v‎$‎. Moreover, we conceptualize and investigate the concept of ‎$‎(u,v)‎$‎-absorbing prime hyperideals as an extension of the $‎(u,v)‎$‎-absorbing hyperideals. We give an example of a ‎$‎(u,v)‎$‎-absorbing prime hyperideal in ‎$‎A‎$‎ that is not a $‎(u,v)‎$‎-absorbing hyperideal. ‎We provide some characterizations of these new notions.

Keywords


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