Related papers: Groebner-Shirshov bases for free inverse semigroup…
We show that every closed normal subgroup of infinite index in a profinite surface group $\Gamma$ is contained in a semi-free profinite normal subgroup of $\Gamma$. This answers a question of Bary-Soroker, Stevenson, and Zalesskii.
'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting of seminearrings in [[16], Mukherjee (Pal) et al., Semigroup…
Chen, Fox, Lyndon 1958 \cite{CFL58} and Shirshov 1958 \cite{Sh58} introduced non-associative Lyndon-Shirshov words and proved that they form a linear basis of a free Lie algebra, independently. In this paper we give another approach to…
This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way…
With each semigroup one can associate a partial algebra, called the biordered set, which captures important algebraic and geometric features of the structure of idempotents of that semigroup. For a biordered set $\mathcal{E}$, one can…
Inverse graph semigroups were defined by Ash and Hall in 1975. They found necessary and sufficient conditions for the semigroups to be congruence free. In this paper we give a description of congruences on a graph inverse semigroup in terms…
In this paper, by using Gr\"obner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative…
In 1985, Bucher, Ehrenfeucht and Haussler studied derivation relations associated with a given set of context-free rules. Their research motivated a question regarding homomorphisms from the semigroup of all words onto a finite ordered…
We prove that the structure of right generalized inverse semigroups is determined by free \'etale actions of inverse semigroups. This leads to a tensor product interpretation of Yamada's classical struture theorem for generalized inverse…
One of the natural ways to prove that the Hall words (Philip Hall, 1933) consist of a basis of a free Lie algebra is a direct construction: to start with a linear space spanned by Hall words, to define the Lie product of Hall words, and…
We consider a new version of Composition-Diamond Lemma for dialgebras in order to obtain an explicit Groebner-Shirshov basis for HNN-extension of dialgebras and determine a normal form for that.
Graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C*-algebras. This paper has two main goals: first, to provide an abstract characterization of graph inverse semigroups; and…
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
Rewriting for semigroups is a special case of Groebner basis theory for noncommutative polynomial algebras. The fact is a kind of folklore but is not fully recognised. The aim of this paper is to elucidate this relationship, showing that…
This is an overview of the basics of inverse semigroup theory written for the Workshop on Semigroups and Categories held at the University of Ottawa in 2010.
The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such…
We generalise the Milnor-Schwarz lemma to inverse monoids acting on presheaves of geodesic metric spaces. We provide two proofs of this fact: one only uses elementary techniques, inspired by the arguments for group actions on metric spaces;…
We study a question which can be roughly stated as follows: Given a (unital or nonunital) algebra $A$ together with a Gr\"obner-Shirshov basis $G$, consider the free operated algebra $B$ over $A$, such that the operator satisfies some…
Assume that $S$ is a semigroup generated by $\{x_1,...,x_n\}$, and let $\Uscr$ be the multiplicative free commutative semigroup generated by $\{u_1,...,u_n\}$. We say that $S$ is of \emph{$I$-typ}e if there is a bijection $v:\Uscr\r S$ such…
We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse…