Related papers: Two-sided expansions of monoids
We investigate the (separated) monomorphism category $\operatorname{mono}(Q,\Lambda)$ of a quiver $Q$ over an Artin algebra $\Lambda$. We construct an epivalence from $\overline{\operatorname{mono}}(Q,\Lambda)$ to…
We show that the membership problem in a finitely generated submonoid of a graph group (also called a right-angled Artin group or a free partially commutative group) is decidable if and only if the independence graph (commutation graph) is…
It is known that each word of length $n$ contains at most $n+1$ distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite…
It is well-known that small categories have equivalent descriptions as partial monoids. We provide a formulation of partial monoid and partial monoid homomorphism involving $s$ and $t$ instead of identities and then following a recent…
In this paper, we introduce PM-mapping class monoids. Braid groups and mapping class groups have many features in common. Similarly to the notion of braid PM-monoid, PM-mapping class monoid is defined. This construction is an analogy of…
We show that the category of $X$-generated $E$-unitary inverse monoids with greatest group image $G$ is equivalent to the category of $G$-invariant, finitary closure operators on the set of connected subgraphs of the Cayley graph of $G$.…
Let $S$ be an unramified regular local ring of mixed characteristic two and $R$ the integral closure of $S$ in a biquadratic extension of its quotient field obtained by adjoining roots of sufficiently general square free elements $f,g\in…
Recently, in weighted automata theory the weight structure of strong bimonoids has found much interest; they form a generalization of semirings and are closely related to near-semirings studied in algebra. Here, we define polynomials over a…
Birman, Ko and Lee have introduced a new monoid ${\cal B}^{*}_{n}$--with an explicit presentation--whose group of fractions is the $n$-strand braid group ${\cal B}_{n}$. Building on a new approach by Digne, Michel and himself, Bessis has…
A commutative cancellative monoid is atomic if every non-invertible element factors into irreducibles (also called atoms), while an integral domain is atomic if its multiplicative monoid is atomic. Back in the eighties, Gilmer posed the…
We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on categories with strict factorization systems. This equivalence is then extended to the category $\mathbf{Mon_s}$ of unital…
This paper investigates the maximal subgroups of a free projection-generated regular $*$-semigroup $PG(P)$ over a projection algebra $P$, and their relationship to the maximal subgroups of the free idempotent-generated semigroup $IG(E)$…
We study the local bihamiltonian structures of the asymmetric rational reductions of the 2D-Toda hierarchy (RR2T) of types $(2,1)$ and $(1,2)$ at the full-dispersive level, and construct a three-dimensional generalized Frobenius manifold…
We introduce a general notion of depth two for ring homomorphism N --> M, and derive Morita equivalence of the step one and three centralizers, R = C_M(N) and C = End_{N-M}(M \o_N M), via dual bimodules and step two centralizers A =…
We show that the freeness problems for automaton semigroups and for automaton monoids are undecidable and, thereby, solve an open problem listed by Grigorchuk, Nekrashevych and Sush\-chansk\u{\i}i. We achieve this using a new technique to…
Free idempotent generated semigroups IG$(E)$, where $E$ is a biordered set, have provided a focus of recent research, the majority of the efforts concentrating on the behaviour of the maximal subgroups. Inspired by an example of Brittenham,…
Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences,…
Skew-monoidal categories arise when the associator and the left and right units of a monoidal category are, in a specific way, not invertible. We prove that the closed skew-monoidal structures on the category of right R-modules are…
For every one-relator monoid $M = \langle A \mid u=v \rangle$ with $u, v \in A^*$ we construct a contractible $M$-CW complex and use it to build a projective resolution of the trivial module which is finitely generated in all dimensions.…
This paper is the second in a series investigating cartesian closed varieties. In first of these, we showed that every non-degenerate finitary cartesian variety is a variety of sets equipped with an action by a Boolean algebra B and a…