相关论文: Survey on generalizations of Hopficity of modules

In this paper, we introduce and study the notion of linkage of modules by reflexive homomorphisms. This notion unifies and generalizes several known concepts of linkage of modules and enables us to study the theory of linkage of modules…

An $R$-module $M$ is Hopfian (co-Hopfian) if any epic (monic) endomorphism of $M$ is an automorphism. If $R$ is commutative Noetherian, we characterize the co-Hopfian injective $R$-modules, and the Hopfian injectives in the case that $R$ is…

We completely describe in certain important cases the class of commutative co-finitely Hopfian groups as defined by Bridson-Groves-Hillman- Martin in the journal Groups, Geometry, and Dynamics on 2010 (see [3]). We also consider and give a…

If $R$ is a ring with 1, we call a unital left $R$-module $M$ co-Hopfian (Hopfian) in the category of left $R$-modules if any monic (epic) endomorphism of $M$ is an automorphism. For commutative Noetherian $R$ we use results of Matlis to…

Let $M$ denote a finitely generated module over a Noetherian ring $R$. For an ideal $I \subset R$ there is a study of the endomorphisms of the local cohomology module $H^g_I(M), g = \operatorname{grade} (I,M),$ and related results. Another…

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…

A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine…

Recently, several authors have adopted new alternative approaches in the study of some classical notions of modules. Among them, we find the notion of subprojectivity which was introduced to measure in a way the degree of projectivity of…

In this paper we review and study $R$-modules $M$ for which $S = End_R(M)$ is commutative. For this, we define the concept of center of modules which is a natural generalization of the center of rings. The properties of center of modules,…

We define, via Gorenstein homomorphisms, a class of local rings over which there exist non-trivial totally reflexive modules. We also provide a general construction of such rings, which indicates their abundance.

Endomorphism rings of modules appear as the center of a ring, as the fix ring of ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain *-prime modules (introduced by Bican et…

We describe a class of multivariate series rings generalizing the usual Robba ring over a p-adic field, and give a basic development of phi-modules over such rings. This makes it possible to give a unified survey of a number of recent…

New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical homological invariants like flat dimension,…

This paper explores the concept of \textbf{co-first modules}, a generalization of coprime modules, through the lens of preradicals in module theory. Building on foundational notions such as second modules and coprime modules, we introduce…

The behaviour under coarsening functors of simple, entire, or reduced graded rings, of free graded modules over principal graded rings, of superfluous monomorphisms and of homological dimensions of graded modules, as well as adjoints of…

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437--445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of…

The codomain category of a generalized homology theory is the category of modules over a ring. For an abelian category A, an A-valued (generalized) homology theory is defined by formally replacing the category of modules with the category…

Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the projective and injective dimensions of a finite module $M$ over a (commutative) Noetherian ring $R$. Second, in the other direction, we…

Different and distinct notions of regularity for modules exist in the literature. When these notions are restricted to commutative rings, they all coincide with the well-known von-Neumann regularity for rings. We give new characterizations…

The moduli spaces refered to are topological spaces whose path components parametrize homotopy types. Such objects have been studied in two separate contexts: rational homotopy types, in the work of several authors in the late 1970's; and…