We prove that the endomorphism monoid of the infinite random graph R contains as a submonoid an isomorphic copy of each countable monoid. As a corollary, the monoid of R does not satisfy any non-trivial semigroup identity. We also prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of the monoid of R.

Cancellative abelian monoids encompass abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Both the AC axioms and the cancellation law are diicult for a general purpose theorem prover, as they create many variants of clauses which contain sums. We describe a reened superposition calculus for cancellative abelian monoids which requires neither explicit infere...

An effective characterization of piecewise testable languages was given by Simon in 1972. A difficult part of the proof is to show that if L has a J -trivial syntactic monoid M(L) then L is k-piecewise testable for a suitable k. By Simon’s original proof, an appropriate k could be taken as two times the maximal length of a chain of ideals in M(L). In this paper we improve this estimate of k usi...

A new digital signature scheme in non-commutative Gaussian monoid is presented. Two algebraic structures are employed: Gaussian monoid and a certain module being compatible with a monoid. For both monoid and module, presentation and action level attributes are defined. Monoid action level is defined as monoid element (word) action on module element as an operator. A module is a set of functions...

We study a monoid associated to complex semisimple Lie algebras, called the quantic monoid. Its monoid ring is shown to be isomorphic to a degenerate quantized enveloping algebra. Moreover, we provide normal forms and a straightening algorithm for this monoid. All these results are proved by a realization in terms of representations of quivers, namely as the monoid of generic extensions of a qu...

We develop the theory of transformation semigroups that have degree 2, is, act by partial functions on a finite set such inverse image points at most two elements. show graph fibers an action gives deep connection between semigroup and theory. It is known Krohn–Rhodes complexity 2 2. monoid continuous maps translational hull appropriate 0-simple semigroup. how group mapping can be considered as...

We study commutation properties of subsets of right-angled Artin groups and trace monoids. We show that if Γ is any graph not containing a four-cycle without chords, then the group G(Γ) does not contain four elements whose commutation graph is a four-cycle; a consequence is that G(Γ) does not have a subgroup isomorphic to a direct product of non-abelian free groups. We also obtain corresponding...