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Let $\hat{R}$ be the $I$-adic completion of a commutative ring $R$ with respect to a finitely generated ideal $I$. We give a necessary and sufficient criterion for the category of perfect complexes over $\hat{R}$ to be equivalent to the…

Commutative Algebra · Mathematics 2024-11-25 Paul Balmer , Beren Sanders

Consider an exact action of discrete group $G$ on a separable $C^*$-algebra $A$. It is shown that the reduced crossed product $A\rtimes_{\sigma, \lambda} G$ is strongly purely infinite - provided that the action of $G$ on any quotient $A/I$…

Operator Algebras · Mathematics 2016-08-03 Eberhard Kirchberg , Adam Sierakowski

We study the relationship between the ultraproduct of a crossed product C*algebra $(A\rtimes_{r}G)^{\omega}$ and the crossed product of an ultraproduct C*algebra $A^{\omega}\rtimes _{r}G$ for a fixed free ultrafilter $\omega$ on…

Operator Algebras · Mathematics 2026-02-24 Zhengyu Fu

This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…

Group Theory · Mathematics 2020-05-26 James East , Nik Ruskuc

Given a unital C*-algebra A, an injective endomorphism \alpha:A --> A preserving the unit, and a conditional expectation E from A to the range of \alpha we consider the crossed-product of A by \alpha relative to the transfer operator…

Operator Algebras · Mathematics 2007-05-23 Ruy Exel

Let $R$ be a commutative ring with. The purpose of this paper is to introduce and investigate cubes-difference factor absorbing ideals of R as a generalization of prime ideals.

Commutative Algebra · Mathematics 2025-07-01 Faranak Farshadifar

In this paper, we introduce multiplicative semiderivation and we investigate the commutativity of semiprime rings satisfying certain conditions and identities involving multiplicative semiderivations on a nonzero ideal I of a ring R.

Rings and Algebras · Mathematics 2017-11-30 Oznur Golbasi , Onur Agirtici

We explain a derived version of the basic construction of localisations of module categories by means of idempotent ideals, which lie at the heart of Faltings' almost ring theory. We use it to provide an example of a commutative algebra in…

Commutative Algebra · Mathematics 2025-10-28 Fabian Hebestreit , Peter Scholze

This is the second part of the paper. Results of the first part about crossed modules are applied here to study of quantum groups in braided categories. Correct cross product in the class of quantum braided groups is built. Criterion when…

High Energy Physics - Theory · Physics 2008-02-03 Yuri Bespalov

We lay out the theory of a multiplicity in the setting of a triangulated category having a central ring action from a graded-commutative ring $R$, in other words, an $R$-linear triangulated category. The invariant we consider is modelled on…

K-Theory and Homology · Mathematics 2025-06-04 Petter Andreas Bergh , David A. Jorgensen , Peder Thompson

We discuss the interplay between K-theoretical dynamics and the structure theory for certain C*-algebras arising from crossed products. For noncommutative C*-systems we present notions of minimality and topological transitivity in the…

Operator Algebras · Mathematics 2015-02-24 Timothy Rainone

In this paper, we give a complete, two-way characterization, of when a noncommutative crossed product $A \rtimes_\lambda G$ is simple, in the case of $G$ being an FC-hypercentral group. This is a large class of amenable groups that contains…

Operator Algebras · Mathematics 2026-01-14 Shirly Geffen , Dan Ursu

For a given inverse semigroup S , we introduce the notion of algebraic crossed product by using a given partial action of S, and we will prove that under some condition it is associative. Also we will introduce the concept of partial…

Operator Algebras · Mathematics 2016-02-26 B. Tabatabaie Shourijeh , S. Moayeri Rahni

A higher dimensional generalization of the cross product is associated with an adequate matrix multiplication. This index-free view allows for a better understanding of the underlying algebraic structures, among which are generalizations of…

General Mathematics · Mathematics 2022-01-24 Peter Lewintan

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…

Commutative Algebra · Mathematics 2011-09-23 Raymond C. Heitmann , David A. Jorgensen

Let $R$ be a ring and let $n\ge 2$. We discuss the question of whether every element in the matrix ring $M_n(R)$ is a product of (additive) commutators $[x,y]=xy-yx$, for $x,y\in M_n(R)$. An example showing that this does not always hold,…

Rings and Algebras · Mathematics 2024-04-30 Matej Brešar , Eusebio Gardella , Hannes Thiel

This paper presents a commutative complex oriented cohomology theory with coefficients the quotient ring of complex cobordism MU$^*[1/2]$ modulo the ideal generated by any subsequence of any polynomial generators in special unitary…

Algebraic Topology · Mathematics 2022-12-29 Malkhaz Bakuradze

We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-like objects in the category of racks, generalizing the…

Quantum Algebra · Mathematics 2014-04-02 Alissa S. Crans , Friedrich Wagemann

In this work we present a new definition to the Partial Crossed Product by actions of inverse semigroups in a C^*-algebra, without using the covariant representations as Sieben did in [5]. Also we present an isomorphism between the partial…

Operator Algebras · Mathematics 2008-05-26 Ruy Exel , Felipe Vieira

In this paper we describe the commutant of an arbitrary subalgebra $A$ of the algebra of functions on a set $X$ in a crossed product of $A$ with the integers, where the latter act on $A$ by a composition automorphism defined via a bijection…

Dynamical Systems · Mathematics 2023-05-31 Christian Svensson , Sergei Silvestrov , Marcel de Jeu