Related papers: Coherency and constructions for monoids
Groups with a topology that is in consistent one way or another with the algebraic structure are considered. Classical groups with a topology are topological, paratopological, semitopological, and quasitopological groups. We also study…
A totally ordered monoid, or tomonoid for short, is a monoid endowed with a compatible total order. We deal in this paper with tomonoids that are finite and negative, where negativity means that the monoidal identity is the top element.…
In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroups with finite Rees or Green index. Specific properties under…
We investigate the preservation of the properties of being finitely generated and finitely presented under both direct and wreath products of monoid acts. A monoid $M$ is said to preserve property $\mathcal{P}$ in direct products if, for…
A finite semigroup is finitely related (has finite degree) if its term functions are determined by a finite set of finitary relations. For example, it is known that all nilpotent semigroups are finitely related. A nilpotent monoid is a…
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal monads and comonads, i.e. monads and comonads in a monoidal category such that the endofunctor of the monad or comonad is a monoidal functor…
We compute coherent presentations of Artin monoids, that is presentations by generators, relations, and relations between the relations. For that, we use methods of higher-dimensional rewriting that extend Squier's and Knuth-Bendix's…
Wright showed that, if a 1-ended simply connected locally compact ANR Y with pro-monomorphic fundamental group at infinity admits a proper Z-action, then that fundamental group at infinity can be represented by an inverse sequence of…
In the paper we introduce a notion of the Bruck-Reilly $\lambda$-polycyclic extension of a monoid $S$ with a homomorphism $\theta$ which is an analogue of the Bruck-Reilly extension of a monoid $S$. We describe idempotens of the semigroup…
We give an elementary proof prove of the preservation of the Noetherian condition for commutative rings with unity $R$ having at least one finitely generated ideal $I$ such that the quotient ring is again finitely generated, and $R$ is…
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…
Let $S$ be a submonoid of a free Abelian group of finite rank. We show that if $k$ is a field of prime characteristic such that the monoid $k$-algebra $k[S]$ is split $F$-regular, then $k[S]$ is a finitely generated $k$-algebra, or…
We study rewriting properties of the column presentation of plactic monoid for any semisimple Lie algebra such as termination and confluence. Littelmann described this presentation using L-S paths generators. Thanks to the shapes of…
Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We…
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…
In this paper we prove that for a monoid $S$, products of indecomposable right $S$-acts are indecomposable if and only if $S$ contains a right zero. Besides, we prove that subacts of indecomposable right $S$-acts are indecomposable if and…
We build on the description of left congruences on an inverse semigroup in terms of the kernel and trace due to Petrich and Rankin. The notion of an inverse kernel for a left congruence is developed. Various properties of both the trace and…
A semigroup is completely simple if it has no proper ideals and contains a primitive idempotent. We say that a completely simple semigroup $S$ is a homogeneous completely simple semigroup if any isomorphism between finitely generated…
Let $K$ be a commutative Noetherian ring with identity, let $A$ be a $K$-algebra, and let $B$ be a subalgebra of $A$ such that $A/B$ is finitely generated as a $K$-module. The main result of the paper is that $A$ is finitely presented…
We call a restriction semigroup almost perfect if it is proper and its least monoid congruence is perfect. We show that any such semigroup is isomorphic to a `$W$-product' $W(T,Y)$, where $T$ is a monoid, $Y$ is a semilattice and there is a…