Related papers: Coherency for monoids and purity for their acts
It is shown that the category of \emph{semi-biproducts} of monoids is equivalent to the category of \emph{pseudo-actions}. A semi-biproduct of monoids is a new notion, obtained through generalizing a biproduct of commutative monoids. By…
This paper studies the zero-classes of monoid semi-congruences, understood as internal reflexive relations on a monoid. Classical examples include normal submonoids, which arise as zero-classes of congruences, and positive cones, which are…
We present an algorithmic approach to the conjugacy problems in monoids and semigroups, using rewriting systems. There is a class of monoids and semigroups that satisfy the condition that the transposi- tion problem and the left and right…
A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform…
The themes of cancellation, internal cancellation, substitution have led to a lot of interesting research in the theory of modules over commutative and noncommutative rings. In this paper, we introduce and study cancellation problem in the…
The aim of this paper is to introduce a new class of Noetherian rings of positive characteristic in terms of perfect closures and study their basic properties. If the perfect closure of a Noetherian ring is coherent, we call it an…
The paper is devoted to the investigation of uniform notion for acts over semigroups perceived as an overclass of subdirectly irreducible acts. We establish conditions to fill the gap between these classes of acts. Besides we prove that…
Consider an algebraic semigroup $S$ and its closed subscheme of idempotents, $E(S)$. When $S$ is commutative, we show that $E(S)$ is finite and reduced; if in addition $S$ is irreducible, then $E(S)$ is contained in a smallest closed…
This paper concerns a class of semigroups that arise as products $US$, associated to what we call `action pairs'. Here $U$ and $S$ are subsemigroups of a common monoid and, roughly speaking, $S$ has an action on the monoid completion $U^1$…
Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we first introduce and study the notions of $s$-pure exact sequences and $s$-absolutely pure modules which extend the classical notions of…
Informally, a homotopy monoid is a monoid-like structure in which properties such as associativity only hold `up to homotopy' in some consistent way. This short paper comprises a rigorous definition of homotopy monoid and a brief analysis…
On an arbitrary meet-semilattice S with 0 we define an orthogonality relation and investigate the lattice Cl(S) of all subsets of S closed under this orthogonality. We show that if S is atomic then Cl(S) is a complete atomic Boolean…
In this paper, among other results, there are described (complete) simple - simultaneously ideal- and congruence-simple - endomorphism semirings of (complete) idempotent commutative monoids; it is shown that the concepts of simpleness,…
In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalise different aspects of unital actions of rings and algebras. We prove that every ideal action is…
If $\mathcal{C}$ is a cocomplete monoidal category in which tensoring from both sides preserves coequalizers, then the category of monoids over $\mathcal{C}$ is cocomplete. The same holds if $\mathcal{C}$ has regular factorizations and…
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…
We study classes of proper restriction semigroups determined by properties of partial actions underlying them. These properties include strongness, antistrongness, being defined by a homomorphism, being an action etc. Of particular interest…
A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a…
We show how topological methods developed in a previous article can be applied to prove new results about topological and homological finiteness properties of monoids. A monoid presentation is called special if the right-hand side of each…
In this paper, considering the geometric equivalence for algebras of a variety $_{S}A$ of S-acts over a monoid S, we obtain representation theorems describing all types of the equivalence classes of geometrically equivalent S-acts of…