Related papers: Factorizations in Modules and Splitting Multiplica…

We consider the derived category of permutation modules over a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the set underlying the tt-spectrum of compact…

Idealization of a module $K$ over a commutative ring $S$ produces a ring having $K$ as an ideal, all of whose elements are nilpotent. We develop a method that under suitable field-theoretic conditions produces from an $S$-module $K$ and…

For a regular normal element in an arbitrary ring, we study the category of its module factorizations. The cokernel functor relates module factorizations with Gorenstein projective components to Gorenstein projective modules over the…

We investigate some general machinery for describing semidualizing modules over generic constructions like ladder determinantal rings with coefficients in a normal domain. We also pose and investigate natural localization questions that…

The notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…

Let $(R,\frak m)$ be a commutative noetherian local ring. In this paper, we prove that if $\frak m$ is decomposable, then for any finitely generated $R$-module $M$ of infinite projective dimension $\frak m$ is a direct summand of (a direct…

In this work we develop some categorical aspects of the double structure of a module.

Let $R$ be a $G$-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded…

In this article, we introduce and study S-comultiplication module which is the dual notion of S-multiplication module.We also characterize certain class of rings-modules such as comultiplication modules,S-second submodules,S-prime…

This short note contains random thoughts about a factorization theorem for closure/interior operators on a powerset which is reminiscent to the notion of resolution for a monad/comonad. The question originated from formal topology but is…

Let R be a commutative ring with identity and M be an R-module. The main purpose of this paper is to introduce and study the notion of $\psi$-second submodules of an R-module M.

Let G be a finite group scheme over an algebraically closed field of positive characteristic. Assume further that the connected component of G is unipotent. It is shown that the projectivity of a rational G-module can be detected on a…

Following Zagier, this work studies the rationality and divisibility of Fourier coefficients of meromorphic Hilbert modular forms associated with real quadratic fields, using theta lifts and weak Maass forms. We establish conditions where…

Here we continue to characterize a recently introduced notion, le-modules $_{R}M$ over a commutative ring $R$ with unity \cite{Bhuniya}. This article introduces and characterizes Zariski topology on the set $Spec(M)$ of all prime submodule…

This paper investigates atomic factorizations in the monoid $\mathcal I(R)$ of nonzero ideals of a multivariate polynomial ring $R$, under ideal multiplication. Building on recent advances in factorization theory for unit-cancellative…

We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…

We define the triangulated category of relative singularities of a closed subscheme in a scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations of the related section of a line bundle, and their analogues…

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. First, we introduce and study the $S$-projective dimensions and $S$-injective dimensions of $R$-modules, and then explore the $S$-global dimension…

We propose a generalization of the factorization method to the case when $\mathcal{G}$ is a finite dimensional Lie algebra such that $\mathcal{G}=\mathcal{G}_0\oplus M \oplus N$ (direct sum of vector spaces), where $\mathcal{G}_0$ is a…

For a commutative unital ring $R$ with fixed ideals $I$ and $J$, we introduce and study $I$-prime $R$-modules and $(I, J)$-prime $R$-modules together with their duals $I$-coprime $R$-modules and $(I,J)$-coprime $R$-modules respectively. We…