Related papers: A guide to closure operations in commutative algeb…
This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…
A commutative algebra is exact if its multiplication endomorphisms are trace-free and is Killing metrized if its Killing type trace-form is nondegenerate and invariant. A Killing metrized exact commutative algebra is necessarily neither…
Let A -> B be a homomorphism of commutative rings. The squaring operation is a functor Sq_{B/A} from the derived category D(B) of complexes B-modules into itself. The squaring operation is needed for the definition of rigid complexes (in…
This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer…
In this paper, we study some properties of the closure operator in the Mac\'ias topology on infinite integral domains. Moreover, under certain conditions, we present topological proofs of the infiniteness of maximal ideals and…
This is an expanded and updated version of a talk given at the Conference on Topics in Geometry and Physics at the University of Southern California, November 6, 1992. It is a survey talk, aimed at mathematicians AND physicists, which…
This paper addresses the isomorphism problem for the universal (nonself-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if…
We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null sets. Our approach is based on the notion of a completion ring for a content $\mu$. With…
We describe the norm-closures of the set $\mathfrak{C}_{\mathfrak{E}}$ of commutators of idempotent operators and the set $\mathfrak{E} - \mathfrak{E}$ of differences of idempotent operators acting on a finite-dimensional complex Hilbert…
The tangled closure of a collection of subsets of a topological space is the largest subset in which each member of the collection is dense. This operation models a logical `tangle modality' connective, of significance in finite model…
Recently, in order to broad the application and theoretical areas of rough sets and matroids, some authors have combined them from many different viewpoints, such as circuits, rank function, spanning sets and so on. In this paper, we…
We continue the study of r-ideals, l-ideals, and HSA's in operator algebras. Some applications are made to the structure of operator algebras, including Wedderburn type theorems for a class of operator algebras. We also consider the…
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…
An expansive, monotone operator is dominating; if it is also idempotent it is a closure operator. Although they have distinct properties, these two kinds of discrete operators are also intertwined. Every closure operator is dominating;…
A commutative ring is said to have ITI with respect to an ideal a if the a-torsion functor preserves injectivity of modules. Classes of rings with ITI or without ITI with respect to certain sets of ideals are identified. Behaviour of ITI…
We characterize the tight closure of graded primary ideals in a homogeneous coordinate ring over an elliptic curve by numerical conditions and we show that it is in positive characteristic the same as the plus closure.
In what follows we generalize the notion of a complemented ring to rings that are not necessarily reduced. We then determine how our concepts fit in with other well-known classes of rings.
Our aim is to study certain algebraic properties of the ring $C(X)_\mathcal{P}$ of real-valued functions on $X$ whose closure of discontinuity set is in an ideal of closed sets. We characterize $\mathcal{P}P$-spaces using $z$-ideals and…
We study operator algebras associated to integral domains. In particular, with respect to a set of natural identities we look at the possible nonselfadjoint operator algebras which encode the ring structure of an integral domain. We show…
Let R be an excellent local ring, m its maximal ideal and I an ideal. Then there exists a positive integer c such that for all integers n, the integral closure of (I + m^n) is contained in m^(n/c) + the integral closure of I. In the proof,…