We develop a counterpart to Garside’s analysis of the braid monoid B n relevant for the monoid MLD that describes the geometry of the left self-distributivity identity. The monoid MLD extends B ∞, of which it shares many properties, with the exception that it is not a direct limit of finitely generated monoids. By introducing a convenient local version of the fundamental elements ∆, we prove th...

P gp := {(a, b)|(a, b) ∼ (c, d) if ∃s ∈ P such that s+ a+ d = s+ b+ c}. The monoid P is called integral if the natural map P → P gp is injective. And it is called saturated if it is integral and satisfies that for any p ∈ P , if n · p ∈ P for some positive integer n then p ∈ P . A monoid P is said to be fine if it is integral and finitely generated. A monoid P is called sharp if there are no ot...

A graph monoid is a commutative monoid for which there is a particularly simple presentation, given in terms of a quiver. Such monoids are known to satisfy various nonstable K-theoretical representability properties for either von Neumann regular rings or C*-algebras. We give a characterization of graph monoids within finitely generated antisymmetric refinement monoids. This characterization is...

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...