Related papers: Coherency and constructions for monoids
A monoid $S$ is right coherent if every finitely generated subact of every finitely presented right $S$-act itself has a finite presentation; it is weakly right coherent if every finitely generated right ideal of $S$ has a finite…
A monoid $S$ is said to be weakly right coherent if every finitely generated right ideal of $S$ is finitely presented as a right $S$-act. It is known that $S$ is weakly right coherent if and only if it satisfies the following conditions:…
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…
We call a semigroup $S$ weakly right noetherian if every right ideal of $S$ is finitely generated; equivalently, $S$ satisfies the ascending chain condition on right ideals. We provide an equivalent formulation of the property of being…
A monoid $S$ is right coherent if every finitely generated subact of every finitely presented right $S$-act is finitely presented. The corresponding notion for a ring $R$ states that every finitely generated submodule of every finitely…
A semigroup $S$ is right noetherian if every right congruence on $S$ is finitely generated. In this paper we present some fundamental properties of right noetherian semigroups, discuss how semigroups relate to their substructures with…
A monoid $S$ is said to be right coherent if every finitely generated subact of every finitely presented right $S$-act is finitely presented. Left coherency is defined dually and $S$ is coherent if it is both right and left coherent. These…
A semigroup $S$ is said to be right pseudo-finite if the universal right congruence can be generated by a finite set $U\subseteq S\times S$, and there is a bound on the length of derivations for an arbitrary pair $(s,t)\in S\times S$ as a…
We call a semigroup $S$ f-noetherian if every right congruence of finite index on $S$ is finitely generated. We prove that every finitely generated semigroup is f-noetherian, and investigate whether the properties of being f-noetherian and…
In this paper, we introduce (Rees) artinian S-acts as those acts that satisfy the descending chain condition on their (Rees) congruences. Then, we show that artinian S-acts are those acts whose all factor acts are finitely (Rees)…
Graph products of monoids provide a common framework for free products and direct products. Trace monoids are graph products of finitely generated free monoids. We investigate the interaction of certain finitary conditions with graph…
The purpose of this paper is to introduce the theory of presentations of monoids acts. We aim to construct `nice' general presentations for various act constructions pertaining to subacts and Rees quotients. More precisely, given an $M$-act…
This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation…
In this paper we characterize the monoid congruences of commutative semigroups by the help of the notion of the separator of subsets of semigroups. We show that every monoid congruence of a commutative semigroup S can be constructed by the…
We study congruences on the partial automorphism monoid of a finite rank free group action. We give a decomposition of a congruence on this monoid into a Rees congruence, a congruence on a Brandt semigroup and an idempotent separating…
We discuss residual finiteness and several related separability conditions for the class of monoid acts, namely weak subact separability, strong subact separability and complete separability. For each of these four separability conditions,…
We prove that the Flat Cover Conjecture holds for the category of (right) acts over any right-reversible monoid $S$, provided that the flat $S$-acts are closed under stable Rees extensions. The argument shows that the class…
With every reduced $E$-Fountain semigroup $S$ which satisfies the generalized right ample condition we associate a category with zero morphisms $\mathcal{C}(S)$. Under some assumptions we prove an isomorphism of $\Bbbk$-algebras $\Bbbk…
We call a semigroup $\mathcal{R}$-noetherian if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on $\mathcal{R}$-classes. We investigate the behaviour of the property of…
We initiate the study of the expansion $\mathcal{S}(M)$ of a monoid $M$ obtained via the semidirect product of $M$ acting naturally on the left of its power set (regarded as a semilattice under union). We term this the `subset expansion' of…