Related papers: Prufer conditions in an amalgamated duplication of…

We say that a commutative ring R satisfies the restricted minimum (RM) condition if for all essential ideals I in R, factor R/I is an Artinian ring. We will focus on Noetherian reduced rings because in this setting known results for RM…

We consider the class of all commutative reduced rings for which there exists a finite subset T of A such that all projections on quotients by prime ideals of A are surjective when restricted to T. A complete structure theorem is given for…

The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via…

Let $R$ be a commutative ring and $g(t) \in R[t]$ a monic polynomial. The commutative ring of polynomials $f(C_g)$ in the companion matrix $C_g$ of $g(t)$, where $f(t)\in R[t]$, is called the Companion Ring of $g(t)$. Special instances…

The aim of this paper is to study the probability that the commutator of an arbitrarily chosen pair of elements, each from two different subrings of a finite non-commutative ring equals a given element of that ring. We obtain several…

Some basic properties of the ring of integers $\mathbb{Z}$ are extended to entire rings. In particular, arithmetic in entire principal rings is very similar than arithmetic in the ring of integers $\mathbb{Z}$. These arithmetic properties…

Let $R$ be a commutative ring with ${\Bbb{A}}(R)$ its set of ideals with nonzero annihilator. In this paper and its sequel, we introduce and investigate the {\it annihilating-ideal graph} of $R$, denoted by ${\Bbb{AG}}(R)$. It is the…

We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…

Let $R=K[x_1,\ldots,x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I$ be a polymatroidal ideal of $R$. In this paper, we provide a comprehensive classification of all unmixed polymatroidal ideals. This work…

In the well-known construction of the field of fractions of an integral domain, division by zero is excluded. We introduce "fracpairs" as pairs subject to laws consistent with the use of the pair as a fraction, but do not exclude…

Let $f: A\rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfert of the property of coherence to the amalgamation $A\bowtie^{f}J$. We provide necessary and sufficient conditions for…

We compute the first Andre-Quillen homology modules for the simple over-rings of integrally closed domains and study an ideal theoretic condition arising from the vanishing of the first homology module.

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…

In this paper we give a characterisation of trivial extension algebras in terms of quivers with relations. This result is based on a explicit description of the ideal of relations of the trivial extension of an algebra, given by the first…

This paper presents a commutative complex oriented cohomology theory with coefficients the quotient ring of complex cobordism MU$^*[1/2]$ modulo the ideal generated by any subsequence of any polynomial generators in special unitary…

We study the relation type question, raised by C. Huneke, which asks whether for a complete equidimensional local ring R there exists a uniform bound for the relation type of parameter ideals. Wang gave a positive answer to this question…

Let J \subseteq I be ideals in a commutative Noetherian ring R, and r,s \geq 0. We say that J is a demotion of I if I^r J^s = I^{r+s} \cap J^s for all r,s \geq 0. In this paper, we mainly aim to explore this notion in polynomial rings. In…

We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum…

We discuss projective equivalence of ideals in Noetherian rings and the existence or failure of existence of projectively full ideals. We describe connections with the Rees valuations and Rees integers of an ideal, and consider the question…

In the article "Non-commutative Grobner bases for commutative algebras", Eisenbud-Peeva-Sturmfels proved a number of results regarding Grobner bases and initial ideals of those ideals in the free associative algebra which contain the…