(Weakly) $(\alpha,\beta)$-prime hyperideals in commutative multiplicative hypeering

descriptionPublicationkeyboard_double_arrow_right Preprint , Article 01 Jan 2024Publisher:Islamic Azad University, Shiraz Branch, Faculty of Science, Department of Mathematics, Shiraz, Iran

Authors: Anbarloei, Mahdi;

arXiv: 2406.01354

(Weakly) $(\alpha,\beta)$-prime hyperideals in commutative multiplicative hypeering

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Abstract

Let $H$ be a commutative multiplicative hyperring and $\alpha, \beta \in \mathbb{Z}^+$. A proper hyperideal $P$ of $H$ is called (weakly) $(\alpha,\beta)$-prime if $x^\alpha \circ y \subseteq P$ for $x,y \in H$ implies $x^\beta \subseteq P$ or $y \in P$. In this paper, we aim to investigate (weakly) $(\alpha,\beta)$-prime hyperideals and then we present some properties of them.

Keywords

Hyperrings, $(\alpha,\beta)$-prime hyperideal, weakly $(\alpha,\beta)$-prime hyperideal, Mathematics - Commutative Algebra, $(\alpha,\beta)$-zero

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