Related papers: A more general framework than the delta-primary hy…
In this paper we aim to introduce some hyperideals such as q-primary, (k,n)-absorbing q-primary, sq-primary, wsq-primary hyperideals.
The aim of this research work is to define and characterize a new class of hyperideals in a Krasner (m,n)-hyperring that we call n-ary J-hyperideals. Also, we study the concept of n-ary delta-J-hyperideals as an expansion of n-ary…
Various classes of hyperideals have been studied in many papers in order to let us fully understand the structures of hyperrings in general. The purpose of this paper is the study of some hyperideals whose concept is created on the basis of…
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…
In this paper, we introduce and study the notion of $n$-ary S-hyperideals in a Krasner $(m,n)$-hyperring
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.
Let R be a Krasner (m,n)-hyperring and S be an n-ary multiplicative subset of R. The purpose of this paper is to introduce the notion of n-ary S-prime hyperideals as a new expansion of n-ary prime hyperideals. Several properties and…
In this paper, we will introduce the notion of (u,v)-absorbing hyperideals in multiplicative hyperrings and we will show some properties of them. Then we extend this concept to the notion of (u,v)-absorbing prime hyperideals and thhen we…
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 $K$…
Let R be a multiplicative hyperring. In this paper, we define the concept of 1-absorbing prime hyperideals which is a generalization of the prime hyperideals. Several properties of the hyperideals are provided. Moreover, we introduce the…
Let R be a multiplicative hyperring with identity. In this paper, we define the concept of J-prime hyperideals which is a generalization of n-hyperideals and we will show some properties of them. Then we extend the notion of J-prime to…
In this paper, we aim to introduce weakly $n$-ary $S$-prime hyperideals in a commutative Krasner $(m,n)$-hyperring.
In this study, we examine some properties of $r$-hyperideals in the commutative Krasner hyperrings. Some properties of $pr$-hyperideals are also studied. The relation between prime hyperideals and $r$-hyperideals is investigated. We show…
Primary hyperideals have been introduced and studied in multiplicative hyperrings. In this paper, we intend to study extensively primary hyperideals of multiplicative hyperrings with absorbing zero and prove some results regarding them.…
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})…
The present paper addresses the notion of $(u,v)$-absorbing primary hyperideals in commutative multiplicative hyperrings.
Multiplicative hyperrings are an important class of algebraic hyperstructures which generalize rings further to allow multiple output values for the multiplication operation. Let R be a commutative multiplicative hyperring. The 2-prime…
In this paper, we study commutative Krasner hyperring with nonzero identity. $\phi$-prime, $\phi$-primary and $\phi$-$\delta$-primary hyperideals are introduced. We intend to extend the concept of $\delta$-primary hyperideals to…
In this paper, the notions of integral closure of hyperrings and hyperideals in a Krasner hyperring $(R, +, \cdot)$ are defined and some basics properties of them are studied. We define also the notion of hypervaluation hyperideals and then…
Krasner F^{(m,n)}-hyperring were introduced and investigated by Farshi and Davvaz. In this paper, our purpose is to define and characterize three classes of F-hyperideals in a Krasner F^{(m,n)}-hyperring, namely, prime F-hyperideals,…