Related papers: t-Class semigroups of Noetherian domains

We give a self-dual t-structure on the derived category of $\mathbb{R}$-constructible sheaves over a Noetherian regular ring by generalizing the notion of t-structure.

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…

A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…

We give an algebraic and self-contained proof of the existence of the so-called Noetherian operators for primary submodules over general classes of Noetherian commutative rings. The existence of Noetherian operators accounts to provide an…

We classify all tilting classes over an arbitrary commutative ring via certain sequences of Thomason subsets of the spectrum, generalizing the classification for noetherian commutative rings by…

An arbitrary group action on an algebra $R$ results in an ideal $\mathfrak{r}$ of $R$. This ideal $\mathfrak{r}$ fits into the classical radical theory, and will be called the radical of the group action. If $R$ is a noetherian algebra with…

We continue the study of intersection algebras $\mathcal B = \mathcal B_R(I, J)$ of two ideals $I, J$ in a commutative Noetherian ring $R$. In particular, we exploit the semigroup ring and toric structures in order to calculate various…

A semigroup prime of a commutative ring $R$ is a prime ideal of the semigroup $(R,\cdot)$. One of the purposes of this paper is to study, from a topological point of view, the space $\scal(R)$ of prime semigroups of $R$. We show that, under…

Let D be an integral domain with quotient field K. For any set X, the ring Int(D^X) of integer-valued polynomials on D^X is the set of all polynomials f in K[X] such that f(D^X) is a subset of D. Using the t-closure operation on fractional…

'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting of seminearrings in [[16], Mukherjee (Pal) et al., Semigroup…

Let $t$ be a positive integer and $\mathcal{A}$ a hereditary abelian category satisfying some finiteness conditions. We define the semi-derived Ringel-Hall algebra of $\mathcal{A}$ from the category $\mathcal{C}_{\mathbb{Z}/t}(\mathcal{A})$…

The class of good semigroups is a class of subsemigroups of $N^h$, that includes the value semigroups of rings associated to curve singularities and their blowups, and allows to study combinatorically the properties of these rings. In this…

Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories behave much better than one would…

In algebraic geometry over a variety of universal algebras $\Theta $, the group $Aut(\Theta ^{0})$ of automorphisms of the category $\Theta ^{0}$ of finitely generated free algebras of $\Theta $ is of great importance. In this paper,…

Given an ample action of an inverse semigroup on a locally compact and Hausdorff topological space, we study the ideal structure of the crossed product algebra associated with it. By developing a theory of induced ideals, we manage to prove…

We introduce and study an abstract class of semirings, which we call exact semirings, defined by a Hahn-Banach-type separation property on modules. Our motivation comes from the tropical semiring, and in particular a desire to understand…

We deal with classes of prime ideals whose associated graded ring is isomorphic to the Rees algebra of the conormal module in order to describe the divisor class group of the Rees algebra and to examine the normality of the conormal module.

Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…

In this paper, our aim is to find the relations amongst the cohomology classes of Brill-Noether subvarieties of the moduli space of semistable bundles over an elliptic curve. We obtain results similar to the Poincar\'e relations on a…

Let h be a regular semisimple element in a complex simple Lie algebra g. Let t be an indeterminate. We consider the "variety" of Iwahori subalgebras of g tensored with power series in t which contain t times h. This variety admits a free…