Related papers: Are complete intersections complete intersections?

Given a 0-dimensional affine K-algebra R=K[x_1,...,x_n]/I, where I is an ideal in a polynomial ring K[x_1,...,x_n] over a field K, or, equivalently, given a 0-dimensional affine scheme, we construct effective algorithms for checking whether…

A ring with a test module of finite upper complete intersection dimension is complete intersection.

For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set theoretic…

This is essentially an erratum, with some example to indicate inconsistencies. Suppose $A=k[X_1, X_2, \ldots, X_n]$ is a polynomial ring over a field $k$. The Complete Intersection conjecture states that, for any ideal $I$ in $A$,…

Let $R$ be a commutative ring with nonzero identity and $I$ a proper ideal of $R$. The {\it ideal-based zero-divisor graph} of $R$ with respect to the ideal $I$, denoted by $\Gamma_I(R)$, is the graph on vertices $\{x \in R\setminus I \mid…

Call a domain $R$ an sQQR-domain if each simple overring of $R$, i.e., each ring of the form $R[u]$ with $u$ in the quotient field of $R$, is an intersection of localizations of $R$. We characterize Pr\"ufer domains as integrally closed…

We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…

We study ideals in a local ring $R$ whose quotient rings induce large homomorphisms of local rings. We characterize such ideals over complete intersections, Koszul rings, and over some classes of Golod rings.

Regularity, complete intersection and Gorenstein properties of a local ring can be characterized by homological conditions on the canonical homomorphism into its residue field (Serre, Avramov, Auslander). It is also known that in positive…

Let $(R,\fm)$ be a local ring and $\fa$ be an ideal of $R$. The inequalities $$\begin{array}{ll} \ \Ht(\fa) \leq \cd(\fa,R) \leq \ara(\fa) \leq l(\fa) \leq \mu(\fa) \end{array}$$ are known. It is an interesting and long-standing problem to…

A digraph is semicomplete if any two vertices are connected by at least one arc and is locally semicomplete if the out-neighbourhood (resp. in-neighbourhood) of any vertex induces a semicomplete digraph. In this paper, we characterize all…

Let R be a commutative ring with identity. In this paper, we introduce and investigate the second ideal intersection graph SII(R) of R with vertices are non-zero proper ideals of R and two distinct vertices I and J are adjacent if and only…

Non-commutative Henselian rings are defined and it is shown that a local ring which is complete and separated in the topology defined by its maximal ideal is Henselian provided that it is almost commutative.

Throughout this abstruct $A$ will denote a noetherian commutative ring of dimension $n$. The paper has two parts. Among the interesting results in Part-1 are the following: 1) {\it suppose that $f_1, f_2, ..., f_r$ (with $r \leq n$) is a…

In this paper, we prove that the Stanley--Reisner ideal of any connected simplicial complex of dimension $\ge 2$ that is locally complete intersection is a complete intersection ideal. As an application, we show that the Stanley--Reisner…

The intersection graph of ideals associated with a commutative unitary ring $R$ is the graph $G(R)$ whose vertices all non-trivial ideals of $R$ and there exists an edge between distinct vertices if and only if the intersection of them is…

We prove that every quasi-complete intersection ideal is obtained from a pair of nested complete intersection ideals by way of a flat base change. As a by-product we establish a rigidity statement for the minimal two-step Tate complex…

Let $R$ be a commutative ring with identity and $T(R)$ its total quotient ring. We extend the notion of well-centered overring of an integral domain to an arbitrary commutative ring and we investigate the transfer of this property to…

In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of $\bz^n\oplus T$ with no invertible elements, where $T$ is a finite abelian…

This work concerns surjective maps $\varphi\colon R\to S$ of commutative noetherian local rings with kernel generated by a regular sequence that is part of a minimal generating set for the maximal ideal of $R$. The main result provides…