相关论文: The radical-annihilator monoid of a ring

Our aim in this paper is to explore semisubtractive ideals of semirings. We prove that they form a complete modular lattice. We introduce Golan closures and prove some of their basic properties. We explore the relations between $Q$-ideals…

Given a commutative Noetherian ring $R$ with total ring of fractions $Q(R)$, and a finitely generated $R$-submodule $M$ of $Q(R)$, we prove an equality between trace ideal, and certain annihilator of Ext and Tor of $M$. As a consequence, we…

\emph{Minkowski rings} are certain rings of simple functions on the Euclidean space $W = {\mathbb{R}}^d$ with multiplicative structure derived from Minkowski addition of convex polytopes. When the ring is (finitely) generated by a set…

Thirty years ago, Huneke (for local rings) and Lyubeznik (in general) conjectured that for all regular rings $R$, the local cohomology modules $H^i_I(R)$ have finitely many associated prime ideals. We prove substantial new cases of their…

We show that perfectoidization can be (almost) calculated by using $p$-root closure in certain cases, including the semiperfectoid case. To do this, we focus on the universality of perfectoidization and uniform completion, as well as the…

Some projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T were constructed in [3]. In this paper we describe their integer cohomology rings by generators and relations.

For a commutative ring R we investigate the property that the sets of minimal primes of finitely generated ideals of R is always finite. We prove this property passes to polynomial ring extensions (in an arbitrary number of variables) over…

In this article, the ring of polynomials is studied in a systematic way through the theory of monoid rings. As a consequence, this study provides natural and canonical approaches in order to find easy and rigorous proofs and methods for…

We use pullbacks of rings to realize the submonoids $M$ of $(\N_0\cup\{\infty\})^k$ which are the set of solutions of a finite system of linear diophantine inequalities as the monoid of isomorphism classes of countably generated projective…

We define a closure operation for ideals in a commutative ring which has all the good properties of solid closure (at least in the case of equal characteristic) but such that also every ideal in a regular ring is closed. This gives in…

Let $(R, \frak m)$ be a Noetherian local ring. This paper deals with the annihilator of Artinian local cohomology modules $H^i_{\frak m}(M)$ in the relation with the structure of the base ring $R$, for non negative integers $i$ and finitely…

We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…

We describe the equivariant cohomology ring of rationally smooth projective embeddings of reductive groups. These embeddings are the projectivizations of reductive monoids. Our main result describes their equivariant cohomology in terms of…

We define topologically semiperfect (complete, separated, right linear) topological rings and characterize them by equivalent conditions. We show that the endomorphism ring of a module, endowed with the finite topology, is topologically…

We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…

We define a notion of a rotund quasi-uniform space and describe a new direct construction of a (right-continuous) quasi-pseudometric on a (rotund) quasi-uniform space. This new construction allows to give alternative proofs of several…

In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then…

In this work we analyze the main properties of the Zariski and maximal spectra of the ring ${\mathcal S}^r(M)$ of differentiable semialgebraic functions of class ${\mathcal C}^r$ on a semialgebraic set $M\subset\mathbb{R}^m$. Denote…

We give a new proof of the simultaneous embedded local uniformization Theorem in zero characteristic for essentially of finite type rings and for quasi excellent rings. The results are a consequence of the simultaneaous monomialization…

We use the rational tableaux introduced by Stembridge to give a bideterminant basis for a normal reductive monoid and for its variety of noninvertible elements. We also obtain a bideterminant basis for the full coordinate ring of the…