Related papers: On Graded Strongly $1$-Absorbing Primary Ideals

The present paper addresses the notion of $(u,v)$-absorbing primary hyperideals in commutative multiplicative hyperrings.

In this paper we introduce and study the notion of a graded nil-good ring which is graded by a group. We investigate extensions of graded nil-good rings to graded group rings, Further, we discuss graded matrix ring extensions and trivial…

Let $R$ be a (commutative Noetherian) local ring of prime characteristic that is $F$-pure. This paper studies a certain finite set ${\mathcal I}$ of radical ideals of $R$ that is naturally defined by the injective envelope of the simple…

In this paper we introduce the concept of a prime radical of an ideal of an L-ring L(mu,R) . Among various results pertaining to this concept, we prove here that prime radicals of an ideal eta, its radical , its semiprime radical S(eta) and…

Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the…

Following G.Szasz [2] a subsemigroup I of semigroup S is called an interior ideal if SIS \subset I. In this paper we explore the classes of regular semigroup and its different subclasses by their interior ideals. Furthermore, we introduce…

Let $\Bbb Z_2:=\Bbb Z/2\Bbb Z$ be the additive group with two elements. In this article, we focus only on $\Bbb Z_2$-graded commutative ring i.e commutative ring $R$ such that $R=R_0\oplus R_1$ as Abelian group and $R_iR_j\subseteq R_{i+j}$…

In this article, we show that Mori domains, pseudo-valuation domains, and $n$-absorbing ideals, the three seemingly unrelated notions in commutative ring theory, are interconnected. In particular, we prove that an integral domain $R$ is a…

In this article, we first generalize Kaplansky's zero-divisor conjecture of group-rings $K[G]$ (with $K$ a field) to the more general setting of $G$-graded rings $R=\bigoplus\limits_{n\in G}R_{n}$ with $G$ a torsion-free group. Then we…

Motivated by situations in which the removal of a zero (a.k.a., an absorbing element) from a semigroup yields a subsemigroup with another zero, sets of quasi-zeros (a.k.a., quasi-absorbing elements) are introduced as well as primitive…

This article aims to solve positively Anderson-Badawi Conjecture of n-Absorbing and strongly n-absorbing ideals of commutative rings in the class of u-rings. The main result extends and recovers Anderson-Badawis related result on Prufer…

The theory of ternary $\Gamma$-semirings extends classical ring and semiring frameworks by introducing a ternary product controlled by a parameter set $\Gamma$. Building on the foundational axioms recently established by Rao, Rani, and…

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…

Let $R$ be a commutative ring with $ 1 \neq 0$. We recall that a proper ideal $I$ of $R$ is called a semiprimary ideal of $R$ if whenever $a,b\in R$ and $ab \in I$, then $a\in \sqrt{I}$ or $b\in \sqrt{I}$. We say $I$ is a {\it weakly…

By definition, an $\m$-primary ideal $I$ in a 2-dimensional regular local ring $(R, \m)$ is contracted if $I=R \cap IR[\m/x]$ for some $x \in \m \setminus \m^2$. Contracted ideals have been introduced by Zariski and used for proving the…

All rings are commutative, and all modules are unital. The purpose of this paper is to investigate the characterizations of weakly pseudo primary 2-absorbing sub-module in terms of some types of modules. We provide characterizations for the…

Let $R$ be a commutative ring, $Y\subseteq \mathrm{Spec}(R)$ and $ h_Y(S)=\{P\in Y:S\subseteq P \}$, for every $S\subseteq R$. An ideal $I$ is said to be an $\mathcal{H}_Y$-ideal whenever it follows from $h_Y(a)\subseteq h_Y(b)$ and $a\in…

Symmetric strongly shifted ideals are a class of monomial ideals which come equipped with an action of the symmetric group and are analogous to the well-studied class of strongly stable monomial ideals. In this paper we focus on algebraic…

For commutative rings with identity, we introduce and study the concept of semi $r$-ideals which is a kind of generalization of both $r$-ideals and semiprime ideals. A proper ideal $I$ of a commutative ring $R$ is called semi $r$-ideal if…

In this paper, we introduce the concept of graded m-nil clean ring to extend the existing notion of graded nil-clean ring introduced in [10]. We explore fundamental properties of these rings, emphasizing the interplay between the identity…