Related papers: Tight closure and continuous closure

We give a canonical construction of a balanced big Cohen-Macaulay algebra for a domain of finite type over $\mathbb C$ by taking ultraproducts of absolute integral closures in positive characteristic. This yields a new tight closure…

We prove the following result. Let f be a continuous function in the closed infinite strip in complex plane. Suppose the restriction of f to every circle inscribed in the strip extends holomorphically inside the circle. Then f is…

Reduced ideals have been defined in the context of integer rings in quadratic number fields, and they are closely tied to the continued fraction algorithm. The notion of this type of ideal extends naturally to number fields of higher…

In the context of a finite measure metric space whose measure satisfies a growth condition, we prove "T1" type necessary and sufficient conditions for the boundedness of fractional integrals, singular integrals, and hypersingular integrals…

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

We present some sufficient conditions for continuity of the mapping $f:\langle X,\tau_X^*\rangle \to \langle Y,\tau_Y^*\rangle$, where $\tau_X^*$ and $\tau_Y^*$ are topologies induced by the local function on $X$ and $Y$, resp. under the…

We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank three.

We introduce a very natural topology on the set of total orderings of monomials of any algebra having a countable basis over a field. This topological space and some notable subspaces are compact. This topological framework allows us to…

We prove an inclusion result for graded dagger closure for primary ideals in symmetric section rings of abelian varieties over an algebraically closed field of arbitrary characteristic.

We obtain tight bounds for the minimal number of generators of an ideal with bounded-degree generators in a polynomial ring $K[X_1,\dots,X_n],$ as well as a sharp quantification of the maximum possible size of a minimal generating set of…

The space $F^p$ ($1<p<\infty$) consists of all holomorphic functions $f$ on the open unit disk $\Bbb D$ such that $ \lim_{r\to 1}(1-r)^{1/q}\log^+M_{\infty}(r,f)=0,$ where $M_{\infty}(r,f)=\max_{\vert z\vert\le r}\vert f(z)\vert$ with…

We present a systematic study for the limit closure $(\underline{x})^{\lim}$ of a sequence of elements $\underline{x}$ (eg. a system of of parameters) in a local ring. Firstly, we answer the question which elements are always contained in…

In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then $R$ is regular. We deduce this using the relationship between multiplicity and various ideal closure operations.

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…

We relativize the notion of a compact object in an abelian category with respect to a fixed subclass of objects. We show that the standard closure properties persist to hold in this case. Furthermore, we describe categorical and…

Let I\subset K[x,y] be a <x,y>-primary monomial ideal where K is a field. This paper produces an algorithm for computing the Ratliff-Rush closure I for the ideal I=<m_0,...,m_{n}> whenever m_{i} is contained in the integral closure of the…

We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [ER21], extending our previous results to the expanded context. We apply…

For every finite closure space $X$ one can define a finite topological space $\operatorname{Top} X$ together with a natural projection $\operatorname{Top} X\longrightarrow X$. This could allow to apply the techniques of topological…

We provide necessary and sufficient conditions for simplicial complexes whose determinantal facet ideals admit reduced Grobner bases under diagonal term orders. Building on and extending foundational results for binomial edge ideals and…

The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful…