相关论文: Completions of Countable Excellent Domains and Cou…

Given a finite family of compact subsets of the complex plane we propose a certificate of mutual non-overlapping with respect to area measure. The criterion is stated as a couple of positivity conditions imposed on a four argument…

A commutative local ring is generally defined to be a complete intersection if its completion is isomorphic to the quotient of a regular local ring by an ideal generated by a regular sequence. It has not previously been determined whether…

It is a well-known and easily established fact that every Euclidean domain is also a principal ideal domain. However, the converse statement is not true, and this is usually shown by exhibiting as a counterexample the ring of algebraic…

It is well known that in the Noetherian local ring with infinite residue field the reduction of $\mm$-primary ideal may be given in the form of a sufficiently general linear combination of its generators. In the paper we give a condition…

We study rings which have Noetherian cohomology under the action of a ring of cohomology operators. The main result is a criterion for a complex of modules over such a ring to have finite injective dimension. This criterion generalizes, by…

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$ and $M$ a finitely generated $R$--module. Let $t$ be a non-negative integer such that $\H^i_\fa(M)$ is $\fa$--cofinite for all $i<t$. It is well--known that…

In this paper, we inspect a relatively unexplored notion of finite generation in semirings, namely semirings in which all congruences are finitely generated. Such semirings are dubbed Congruence Noetherian. After developing sufficient…

Let $R$ be a Noetherian ring, $I$ an ideal of $R$ and $M$ an $R$-module. In this article, we examine the question of whether an arbitrary top local cohomology module, $\operatorname{H}^{\operatorname{cd}(I,M)}_I(M)$, is Artinian, or not.…

We determine when a generalized down-up algebra is a Noetherian unique factorisation domain or a Noetherian unique factorisation ring.

Necessary and sufficient conditions are given for a prime Noetherian algebra K[S] of a submonoid S of a polycyclic-by-finite group G to be a maximal order. These conditions are entirely in terms of the monoid S. This extends earlier results…

We consider trace ideals in Noetherian rings and focus our attention to one-dimensional analytically irreducible local rings. For such rings we classify those Gorenstein rings which admit only a finite number of trace ideals.

Let $A$ be a Noetherian ring and let $I$ be an ideal in $A$. Let $\mathcal{F} = \{ J_n \}_{n \geq 0}$ be a multiplicative filtration of ideals in $A$ such that $\mathcal{R}(\mathcal{F}) = \bigoplus_{n \geq 0} J_n$ is a finitely generated…

In this paper, we construct a local ring $A$ such that the kernel of the map $G_0(A)\subq \to G_0(\hat{A})\subq$ is not zero, where $\hat{A}$ is the comletion of $A$ with respect to the maximal ideal, and $G_0()\subq$ is the Grothendieck…

Let T be a complete local (Noetherian) equidimensional ring with maximal ideal m such that the Krull dimension of T is at least two and the depth of T is at least two. Suppose that no integer of T is a zerodivisor and that |T|=|T/m|. Let d…

The Noetherian type of a space is the least $\kappa$ such that it has a base that is $\kappa$-like with respect to containment. Just as all known homogeneous compacta have cellularity at most $2^\omega$, they satisfy similar upper bounds in…

For a Noetherian commutative ring $R$, let $H^i_I(R)$ be the $ i$-th local cohomology module of $R$ with respect to $I$. In \cite{Hel-08}, Hellus posed the question of identifying rings $R$ such that $\operatorname{injdim}_R…

We use our extension of the Noether-Lefschetz theorem to describe generators of the class groups at the local rings of singularities of very general hypersurfaces containing a fixed base locus. We give several applications, including (1)…

In \cite{AB}, the dagger closure is extended over finitely generated modules over Noetherian local domain $(R,\fm)$ and it is proved to be a Dietz closure. In this short note we show that it also satisfies the `Algebra axiom' of \cite{R.G}…

We prove that a complete local or graded one-dimensional domain of prime characteristic has finite F-representation type if its residue field is algebraically closed or finite, and present examples of a complete local or graded…

We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating…