We introduce and study the partial singular braid monoid PSBn, a monoid that contains both the inverse braid monoid IBn and the singular braid monoid SBn. Our main results include a characterization of Green’s relations, a presentation in terms of generators and relations, and a proof that PSBn embeds in the semigroup algebra C[IBn].

We prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of End(R), the endomorphism monoid of the infinite random graph R. Consequently, End(R) embeds each countable monoid, satisfies no nontrivial monoid identity, and has an undecidable universal theory.

We generalize the notion of a coloring complex graph to linearized combinatorial Hopf monoids. determine when monoid has such construction, and discover some inequalities that are satisfied by quasisymmetric function invariants associated monoid. show collection all complexes forms monoid, which is terminal object in category monoids with convex characters. also study several examples

We prove that a trace monoid embeds into the queue monoid if and only if it embeds into the direct product of two free monoids. We also give a decidable characterization of these trace monoids.

A monoid hypersurface is an irreducible hypersurface of degree d which has a singular point of multiplicity d−1. Any monoid hypersurface admits a rational parameterization, hence is of potential interest in computer aided geometric design. We study properties of monoids in general and of monoid surfaces in particular. The main results include a description of the possible real forms of the sing...

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...