We introduce the notion of an orthogonal completion of an inverse monoid with zero. We show that the orthogonal completion of the polycyclic monoid on n generators is isomorphic to the inverse monoid of right ideal isomorphisms between the finitely generated right ideals of the free monoid on n generators, and so we can make a direct connection with the Thompson groups Vn,1. 2000 AMS Subject Cl...

On Graphs With A Given Endomorphism Monoid Benjamin Shemmer Hedrĺın and Pultr proved that for any monoid M there exists a graph G with endomorphism monoid isomorphic to M. We will give a construction G(M) for a graph with prescribed endomorphism monoid M. Using this construction we derive bounds on the minimum number of vertices and edges required to produce a graph with a given endomorphism mo...

We introduce a ramified monoid , attached to each Brauer–type monoid, that is, the symmetric group Jones and Brauer monoids among others. Ramified correspond class of tied arising from knot theory are interesting in themselves. The is Coxeter-like version so–called braid monoid. give presentation Also, we study two tied-like cannot be described as monoids. However, these can also regarded versi...

We present three results on divisibility monoids. These divisibility monoids were introduced in [11] as an algebraic generalization of Mazurkiewicz trace monoids. (1) We give a decidable class of presentations that gives rise precisely to all divisibility monoids. (2) We show that any divisibility monoid is an automatic monoid [5]. This implies that its word problem is solvable in quadratic tim...

The main result of this paper gives a presentation for an arbitrary subgroup of a monoid defined by a presentation. It is a modification of the well known Reidemeister–Schreier theorem for groups. Some consequences of this result are explored. It is proved that a regular monoid with finitely many left and right ideals is finitely presented if and only if all its maximal subgroups are finitely p...

A monoid M is a Cale monoid with base Q if for every nonunit x ∈ M there exists a positive integer n such that xn factors uniquely up to order and associates as elements from Q ⊆ M\M. An integral domain D is a Cale domain with base Q, if its multiplicative monoid of nonzero elements is a Cale monoid with base Q. We explore the basic properties of Cale monoids and integral domains. In particular...

This paper proves that any monoid presented by a confluent context-free monadic rewriting system is word-hyperbolic. This result then applied to answer a question asked by Duncan&Gilman by exhibiting an example of a word-hyperbolic monoid that does not admit a word-hyperbolic structure with uniqueness (that is, in which the language of representatives maps bijectively onto the monoid).

We study the geometry of algebraic monoids. We prove that the group of invertible elements of an irreducible algebraic monoid is an algebraic group, open in the monoid. Moreover, if this group is reductive, then the monoid is affine. We then give a combinatorial classification of reductive monoids by means of the theory of spherical varieties.

We describe a new monoid structure for braid groups associated with finite Coxeter systems. This monoid shares with the classical positive braid monoid its crucial algebraic properties: the monoid satisfies Öre’s conditions and embeds in its group of fractions, it admits a nice normal form, it can be used to construct braid group actions on categories... It also provides a new presentation for ...