Related papers: Classical and strongly classical 2-absorbing secon…
Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…
The aim of this paper is to investigate properties of endo-prime and endo-coprime modules which are generalizations of prime and simple rings, respectively. Various properties of endo-coprime modules are obtained. Duality-like connections…
In this work, we introduce the notion of $S$-1-absorbing primary submodule as an extension of 1-absorbing primary submodule. Let $S$ be a multiplicatively closed subset of a ring $R$ and $M$ be an $R$-module. A submodule $N$ of $M$ with…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
We study the problem of classification of simple transitive 2-representations for the (non-finitary) 2-category of bimodules over the dual numbers. We show that simple transitive 2-representations with finitary apex are necessarily of rank…
Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we first introduce and study the notions of $s$-pure exact sequences and $s$-absolutely pure modules which extend the classical notions of…
This paper introduces and studies a particular subclasses of the class of commutative rings with finite Gorenstein global (resp., weak) dimensions.
We study the dual algebras of (discrete) Hopf algebroids. In particular, we understand comodules over a Hopf algebroid as (discrete) modules over its dual algebra.
We show that various derived categories of torsion modules and contramodules over the adic completion of a commutative ring by a weakly proregular ideal are full subcategories of the related derived categories of modules. By the work of…
In this paper we introduce principal 2-bundles and show how they are classified by non-abelian Cech cohomology. Moreover, we show that their gauge 2-groups can be described by 2-group-valued functors, much like in classical bundle theory.…
This note gives a unifying characterization and exposition of strongly irreducible elements and their duals in lattices. The interest in the study of strong irreducibility stems from commutative ring theory, while the dual concept of strong…
In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting…
Tilting modules over commutative rings were recently classified in [12]: they correspond bijectively to faithful Gabriel topologies of finite type. In this note we extend this classification by dropping faithfulness. The counterpart of an…
Given two C*-algebras A and B, abstract A-B bimodules that can be isometrically represented as operator bimodules are characterised in terms of their norm. Various properties of such bimodules are given. Their theory is very similar to…
Many two-dimensional classical field theories have hidden symmetries that form an infinite-dimensional algebra. For those examples that correspond to effective descriptions of compactified superstring theories, the duality group is expected…
We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n-1 symmetries polynomial in the canonical momenta, so that they are in…
A depth two extension $A \| B$ is shown to be weak depth two over its double centralizer $V_A(V_A(B))$ if this is separable over $B$. We consider various examples and non-examples of depth one and two properties. Depth two and its…
The aim of the paper is to classify the indecomposable modules and describe the Auslander--Reiten sequences for admissible algebras with formal two-ray modules.