Related papers: Some generalizations of second submodules

We study the construction and properties of modules whose endomorphism rings have a unique two-sided maximal ideal.

We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral…

In this work we generalize the concept of injective module and develop a theory of divisibility for modules over a general ring, which provides a general and unified framework to study Kummer-like field extensions arising from commutative…

Generalizing differential geometry of smooth vector bundles formulated in algebraic terms of the ring of smooth functions, its derivations and the Koszul connection, one can define differential operators, differential calculus and…

This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…

In this paper we introduce topological modules over the ring of bihyperbolic numbers. We discuss bihyperbolic convexity, bihyperbolic-valued seminorms and bihyperbolic-valued Minkowski functionals in topological bihyperbolic modules.…

We consider a generalisation of the specialisation functor on Soergel bimodules and show that this generalised version still takes Soergel bimodules to Soergel modules.

This paper extends Auslander-Reiten duality in two directions. As an application, we obtain various criteria for freeness of modules over local rings in terms of vanishing of Ext modules, which recover a lot of known results on the…

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with identity and $M$ a graded $R$-module. In this paper, we introduce the concept of graded $I_{e}$-prime submodule as a generalization of a graded prime…

Let $D$ be a division ring. In this paper, we investigate properties of subgroups of an arbitrary subnormal subgroup of the multiplicative group $D^*$ of $D$. The new obtained results generalize some previous results on subgroups of $D^*$.

In representation theory, the double centraliser property is an important property for a module (bimodule). It plays a fundamental role in many theories. In this paper, we extend this property to complexes in derived categories of finite…

This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes…

We exhibit a correspondence between subcategories of modules over an algebra and sub-bimodules of the dual of that algebra. We then prove that the semisimplicity of certain such categories is equivalent to the existence of a Peter-Weyl…

Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…

We study basic properties of the generalized ideal transforms $D_I(M, N)$ and the set of associated primes of the modules $R^iD_I(M,N).$

In a general algebraic setting, we state some properties of commutators of reflexive admissible relations.

Researchers introduced the notion of j-Artinian rings in [3] and obtained significant results concerning this new class of rings. Motivated by their definition and findings, we extend the study to modules by introducing the concept of…

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…

The support of any module over a commutative ring is defined as the collection of all prime ideals of the ring at which the localization of the module is non-zero. For finitely generated modules, the support is the collection of all prime…

A semi-dualizing module over a commutative noetherian ring A is a finitely generated module C with RHom_A(C,C) \simeq A in the derived category D(A). We show how each such module gives rise to three new homological dimensions which we call…