Related papers: Fundamental Results on $s$-Closures

The closed one-sided ideals of a C*-algebra are exactly the closed subspaces supported by the orthogonal complement of a closed projection. Let A be a (not necessarily selfadjoint) subalgebra of a unital C*-algebra B which contains the unit…

We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning…

A multiplicative hyperring is a well-known type of algebraic hyperstructures which extend a ring to a structure in which the addition is an operation but multiplication is a hyperoperation. Let G be a commutative multiplicative hyperring…

In this paper, we introduce the concept of S-J-ideals in both commutative and noncommutative rings. For a commutative ring R and a multiplicatively closed subset S, we show that many properties of J-ideals apply to S-J-ideals and examine…

Let A be a Noetherian ring and B be a finitely generated A-algebra. Denote by A' the integral closure of A in B. We give necessary and sufficient conditions for prime ideals to be in Ass_{A}(B/A') and Ass_{A'}(B/A') generalizing and…

We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is a orthonormal basis for the inner product of…

We look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the non-homogeneous m-coprimary case in standard graded rings. Although our…

The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains…

This paper is concerned with the prime spectrum of a tensor product of algebras over a field. It seeks necessary and sufficient conditions for such a tensor product to have the S-property, strong S-property, and catenarity. Its main results…

Motivated by closed string perturbation theory arguments by S. Shenker, we consider non-perturbative effects of characteristic strength $\mathcal{O}(e^{-1/g_{s}})$, with $g_{s}$ the closed string coupling constant, in supersymmetric…

We prove that the tight closure and the graded plus closure of a homogeneous ideal coincide for a two-dimensional N-graded domain of finite type over the algebraic closure of a finite field. This answers in this case a ``tantalizing…

A graph is closed when its vertices have a labeling by $[n]$ such that the binomial edge ideal $J_G$ has a quadratic Gr\"{o}bner basis with respect to the lexicographic order induced by $x_1 > \cdots > x_n > y_1> \cdots > y_n$. In this…

Let $S$ be the power series ring or the polynomial ring over a field $K$ in the variables $x_1,\ldots,x_n$, and let $R=S/I$, where $I$ is proper ideal which we assume to be graded if $S$ is the polynomial ring. We give an explicit…

This paper exhibits some new examples of the behavior of the Castelnuovo-Mumford regularity of homogeneous ideals in polynomial rings. More precisely, we present new examples of homogenous ideals with large regularity compared to the…

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see,…

In this paper, we elaborate ring theoretic properties of nodal orders. In particular, we prove that they are closed under taking crossed products with finite groups.

Hochster and Huneke proved in \cite{HH5} fine behaviors of symbolic powers of ideals in regular rings, using the theory of tight closure. In this paper, we use generalized test ideals, which are a characteristic $p$ analogue of multiplier…

In this work we study the classes of epsilon and nearly epsilon-strongly graded rings by a group $G$. In particular, we extend Dade's theorem to the realm of nearly epsilon-strongly graded rings. Moreover, we introduce the category…

We use geometric and cohomological methods to show that given a degree bound for membership in ideals of a fixed degree type in the polynomial ring P=k[x_0,..., x_d], one obtains a good generic degree bound for membership in the tight…

In this paper we study strongly hollow ideals and completely strongly hollow ideals in commutative rings without finiteness assumptions. We establish basic structural properties, including maximality phenomena and permanence under quotients…