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Mahdi Anbarloei

Publications and source records attributed to Mahdi Anbarloei.

At least 19 recordsLinked to original sources
arXiv2026

On n-ary S-hyperideals

In this paper, we introduce and study the notion of $n$-ary S-hyperideals in a Krasner $(m,n)$-hyperring

math.AC↗
arXiv2025

Quasi S-primary hyperideals

In this paper, we define and study quasi S-primary hyperideals, weakly quasi S-hyperideals and strongly S-primary hyperideals.

math.AC↗
arXiv2024

$ϕ$-$δ$-$S$-primary hyperideals

Among many generalizations of primary hyperideals, weakly $n$-ary primary hyperideals and $n$-ary $S$-primary hyperideals have been studied recently. Let $S$ be an $n$-ary multiplicative set of a commutative Krasner $(m,n)$-hyperring $K$ and, $ϕ$ and $δ$ be reduction and expansion functions of hyperideals of $K$, respectively. The purpose of this paper is to introduce $n$-ary $ϕ$-$δ$-$S$-primary hyperideals which serve as an extension of $S$-primary hyperideals with the help of $ϕ$ and $δ$. We present some main results and examples explaining the sructure of this concept. We examine the relations of $n$-ary $S$-primary hyperideals with other classes of hyperideals and give some ways to connect them. Moreover, we give some characterizations of this notion on direct product of commutative Krasner $(m, n)$-hyperrings.

math.AC↗
arXiv2024

On weakly S-primary hyyperideals

In this paper, our purpose is to introduce and study the notion of weakly n-ary S-primary hyperideals in a commutative Krasner (m,n)-hyperring.

math.AC↗
arXiv2024

Weakly S-prime hyperideals

In this paper, we aim to introduce weakly $n$-ary $S$-prime hyperideals in a commutative Krasner $(m,n)$-hyperring.

math.AC↗
arXiv2024

(Weakly) $(α,β)$-prime hyperideals in commutative multiplicative hypeering

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

math.AC↗
arXiv2024

Merging N-hyperideals and J-hyperideals in one frame

The notions of N-hyperideals and J-hyperideals as two classes of hyperideals were recently defined in the context of Krasner (m,n)-hyperrings. These concepts are created on the basis of the intersection of all n-ary prime hyperideals and the intersection of all maximal hyperideals, respectively. Despite being vastly different in many aspects, they shar numerous similar properties. The aim of this research work is to merge them under one frame called n-ary delta(0)-hyperideals where the function delta assigns to each hyperideals of a Krasner (m,n)-hyperring a hyperideal of the same hyperring. We give various properties of n-ary delta(0)-hyperideals and use them to characerize certain classes of hyperring such as hyperintegral domains and local hyperrings. Moreover, we introduce the notions of (s,n)-absorbing delta(0)-hyperideals and weakly (s,n)-absorbing delta(0)-hyperideals.

math.AC↗
arXiv2023

(weakly) (s,n)-closed hyperideals

A multiplicative hyperring is a well-known type of algebraic hyperstructures which extend a ring to a structure in which the addition is an operation but multiplication is a hyperoperation. Let G be a commutative multiplicative hyperring and s,n \in Z^+. A proper hyperideal Q of G is called (weakly) (s,n)-closed if (0 \neq a^s \subseteq Q) s^s \subseteq Q for a\in G implies a^n \subseteq Q. In this paper, we aim to investigate (weakly) (s,n)-closed hyperideals and give some results explaining the structures of these notions.

math.RA↗
arXiv2023

$ϕ$-$(k,n)$-absorbing and $ϕ$-$(k,n)$-absorbing primary hyperideals in a krasner $(m,n)$-hyperring

Various expansions of prime hyperideals have been studied in a Krasner $(m,n)$-hyperring $R$. For instance, a proper hyperideal $Q$ of $R$ is called weakly $(k,n)$-absorbing primary provided that for $r_1^{kn-k+1} \in R$, $g(r_1^{kn-k+1}) \in Q-\{0\}$ implies that there are $(k-1)n-k+2$ of the $r_i^,$s whose $g$-product is in $Q$ $g(r_1^{(k-1)n-k+2}) \in Q$ or a $g$-product of $(k-1)n-k+2$ of $r_i^,$s ,except $g(r_1^{(k-1)n-k+2})$, is in ${\bf r^{(m,n)}}(Q)$. In this paper, we aim to extend the notions to the concepts of $ϕ$-$(k,n)$-absorbing and $ϕ$-$(k,n)$-absorbing primary hyperideals. Assume that $ϕ$ is a function from $ \mathcal{HI}(R)$ to $\mathcal{HI}(R) \cup \{\varnothing\}$ such that $\mathcal{HI}(R)$ is the set of hyperideals of $R$ and $k$ is a positive integer. We call a proper hyperideal $Q$ of $R$ a $ϕ$-$(k,n)$-absorbing primary hyperideal if for $r_1^{kn-k+1} \in R$, $g(r_1^{kn-k+1}) \in Q-ϕ(Q)$ implies that there are $(k-1)n-k+2$ of the $r_i^,$s whose $g$-product is in $Q$ $g(r_1^{(k-1)n-k+2}) \in Q$ or a $g$-product of $(k-1)n-k+2$ of $r_i^,$s ,except $g(r_1^{(k-1)n-k+2})$, is in ${\bf r^{(m,n)}}(Q)$. Several properties and characterizations of them are presented.

math.AC↗