An Approach to Injective Acts over Monoids Based on Indecomposability

星图的偏满射的生成元问题

Presentations for monoids of partial endomorphisms of a star graph

本文研究星图的各类偏满射的生成元问题，通过构造不同类型的偏满射的生成元来描述其结构。

Preenveloping Classes of Acts

Preenvelopes of acts over a monoid are defined by analogy with Enochs' definition of preenvelopes of modules. Provided that it is closed for pure subacts, a class of acts is shown to be preenveloping precisely when it is closed under direct products. Examples of such classes include absolutely pure, weakly f-injective and weakly p-injective acts.

Coherency for monoids and purity for their acts

This article examines the three-way relationship between right coherency of a monoid $S$, solutions of equations over $S$-acts, and injectivity properties of $S$-acts. A monoid $S$ is right coherent if every finitely generated subact of every finitely presented (right) $S$-act itself has a finite presentation. Purity properties of an $S$-act $A$ may either be expressed in terms of solutions in $A$ of certain consistent sets of equations over $A$, or in terms of injectivity properties. For example, an $S$-act $A$ is absolutely pure (almost pure) if every finite consistent set of equations over …

Finiteness conditions of $S$-Cohn-Jordan Extensions

Let a monoid $S$ act on a ring $R$ by injective endomorphisms and $A=A(R,S)$ denote the $S$-Cohn-Jordan extension of $R$. Some results relating finiteness conditions of $R$ and that of $A$ are presented. In particular necessary and sufficient conditions for $A$ to be left noetherian, to be left Bézout and to be left principal ideal ring are presented.

Covers of acts over monoids and pure epimorphisms

In 2001 Enoch's celebrated flat cover conjecture was finally proven and the proofs (two different proofs were presented in the same paper [4]) have since generated a great deal of interest among researchers. In particular the results have been recast in a number of other categories and in particular for additive categories (see for example [2], [3], [22] and [23]). In 2008, Mahmoudi and Renshaw considered a similar problem for acts over monoids but used a slightly different definition of cover. They proved that in general their definition was not equivalent to Enoch's, except in the projective…

星形图的部分自同态研究

On partial endomorphisms of a star graph

该文针对有限顶点星形图，系统研究五类部分自同态幺半群的秩、Green关系、基数与正则性。