Related papers: On the arithmetic of stable domains

A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…

Simple-minded systems in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Simple-minded systems are shown to be invariant…

Among the finitely generated modules over a Noetherian ring R, the semidualizing modules have been singled out due to their particularly nice duality properties. When R is a normal domain, we exhibit a natural inclusion of the set of…

We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids. When R=$\mathbb{Z}$, and when R is a DVR, we get…

Purpose: To develop the algebraic foundation of finite commutative ternary $\Gamma$-semirings by identifying their intrinsic invariants, lattice organization, and radical behavior that generalize classical semiring and $\Gamma$-ring…

There has arisen in recent years a substantial theory of "multiplier ideals'' in commutative rings. These are integrally closed ideals with properties that lend themselves to highly interesting applications. But how special are they among…

Let $R=\oplus_{m\geq 0}R_m$ be a standard graded equidimensional ring over a field $R_0$, and $I\subseteq J$ be two non-nilpotent graded ideals in $R$. Then we give a set of numerical characterizations of the integral dependence of $I$ and…

We call a ring R pointwise semicommutative if for any element a in R either l(a) or r(a) is an ideal of R. A class of pointwise semicommutative rings is a strict generalization of semicommutative rings. Since reduced rings are pointwise…

We study the problem of $\mathfrak{m}$-adic stability of F-singularities, that is, whether the property that a quotient of a local ring $(R,\mathfrak{m})$ by a non-zero divisor $x \in \mathfrak{m}$ has good F-singularities is preserved in a…

We analyze stable homology over associative rings and obtain results over Artin algebras and commutative noetherian rings. Our study develops similarly for these classes; for simplicity we only discuss the latter here. Stable homology is a…

A pair of elements $a,b$ in an integral domain $R$ is an idempotent pair if either $a(1-a) \in bR$, or $b(1-b) \in aR$. $R$ is said to be a PRINC domain if all the ideals generated by an idempotent pair are principal. We show that in an…

An ideal I of a commutative ring R is said to be irreducible if it cannot be written as the intersection of two larger ideals. A proper ideal I of a ring R is said to be strongly irreducible if for each ideals J, K of R, J\cap K\subseteq I…

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we introduce the cozero-divisor graph $\acute{\Gamma}_I(R)$ of $R$ and obtain some related results.

Let $R$ be a commutative ring with unity. The prime ideal sum graph of the ring $R$ is the simple undirected graph whose vertex set is the set of all nonzero proper ideals of $R$ and two distinct vertices $I$, $J$ are adjacent if and only…

We consider a rational map f:S->S of a complex projective surface together with an invariant meromorphic two form. Under a mild topological assumption on the map, we show that the zeroes of the invariant form can be eliminated by birational…

Let $R$ be a commutative ring and $M$ be an $R$-module, and let $Z(M)$ be the set of all zero-divisors on $M$. In 2008, D.F. Anderson and A. Badawi introduced the regular graph of $R$. In this paper, we generalize the regular graph of $R$…

In this paper using the connections between some subvarieties of residuated lattices, we investigated some properties of the lattice of ideals in commutative and unitary rings. We give new characterizations for commutative rings $A$ in…

We introduce the concept of monomial ideals with stable projective dimension, as a generalization of the Cohen-Macaulay property. Indeed, we study the class of monomial ideals $I$, whose projective dimension is stable under monomial…

The purpose of this work is to extend the study of the commutative rings whose lattice of ideals can be a structure of BL-algebra as carry out by Heubo et al in 2018, to non commutative rings appointed in the work as pseudo BL-rings. We…

A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…