Related papers: Binary modules and their endomorphisms

We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain "generic" Hecke algebra, infinite-dimensional in general, coming from the universal enveloping algebra…

We give a parametrization of the ideal classes of rings associated to integral binary forms by classes of tensors in $\mathbb Z^2\tensor \mathbb Z^n\tensor \mathbb Z^n$. This generalizes Bhargava's work on Higher Composition Laws, which…

We study the category $\operatorname{Morph}(\operatorname{Mod} R)$ whose objects are all morphisms between two right $R$-modules. The behavior of objects of $\operatorname{Morph}(\operatorname{Mod} R)$ whose endomorphism ring in…

We introduce a generalization of the notion of a negligible morphism and study the associated tensor ideals and thick ideals. These ideals are defined by considering deformations of a given monoidal category $\mathcal{C}$ over a local ring…

This paper investigates the application of the theoretical algebraic notion of a separable ring extension, in the realm of cyclic convolutional codes or, more generally, ideal codes. We work under very mild conditions, that cover all…

To each finitely presented module M over a commutative ring R one can associate an R-ideal Fit_R(M) which is called the (zeroth) Fitting ideal of M over R and which is always contained in the R-annihilator of M. In an earlier article, the…

Let $R$ be a commutative ring, $M$ an $R$-module and $\varphi_a$ be the endomorphism of $M$ given by right multiplication by $a\in R$. We say that $M$ is {\it weakly-morphic} if $M/\varphi_a(M)\cong \ker(\varphi_a)$ as $R$-modules for every…

We give a categorical description of all abelian varieties with commutative endomorphism ring over a finite field with $q=p^a$ elements in a fixed isogeny class in terms of pairs consisting of a fractional $\mathbb Z[\pi,q/\pi]$-ideal and a…

Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences,…

Let $\mathbb{F}_q[T]$ be the polynomial ring over a finite field $\mathbb{F}_q$. We study the endomorphism rings of Drinfeld $\mathbb{F}_q[T]$-modules of arbitrary rank over finite fields. We compare the endomorphism rings to their subrings…

Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the semidualizing modules, we define and study new classes of modules and homological dimensions and investigate the relations between them. In…

Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S =$ End$_R(M)$. In this paper we introduce dual $\pi$-Rickart modules as a generalization of $\pi$-regular rings as well as that of dual Rickart modules. The…

We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank three.

We introduce a procedure based on computational algebraic geometry to determine whether two algebras are isomorphic. We then apply it to show that if $R$ is a commutative unital ring in which $2$ is not invertible, $G$ is a group of order…

By Rickard's work, two rings are derived equivalent if there is a tilting complex, constructed from projective modules over the first ring such that the second ring is the endomorphism ring of this tilting complex. In this work I describe,…

Commutative semirings with divisible additive semigroup are studied. We show that an additively divisible commutative semiring is idempotent, provided that it is finitely generated and torsion. In case that a one-generated additively…

We prove that for a countable, commutative ring $R$, the class of countable $R$-modules either has only countably many isomorphism types, or else it is Borel complete. The machinery gives a succinct proof of the Borel completeness of TFAB,…

Given $r \in \mathbf{N},$ let $\lambda$ be a partition of $r$ with at most two parts. Let $\mathbf{F}$ be a field of characteristic 3. Write $M^\lambda$ for the $\mathbf{F}S_r$-permutation module corresponding to the action of the symmetric…

Let R be a ring, M a nonzero left R-module, X an infinite set, and E the endomorphism ring of the direct sum of copies of M indexed by X. Given two subrings S and S' of E, we will say that S is equivalent to S' if there exists a finite…

The notion of ring endomorphisms having large images is introduced. Among others, injectivity and surjectivity of such endomorphisms are studied. It is proved, in particular, that an endomorphism S of a prime one-sided noetherian ring R is…