An algebra M = (M ; ,∨,∧,→, 0, 1) of type 〈2, 2, 2, 2, 0, 0〉 is called a bounded commutative R`-monoid iff (i) (M ; , 1) is a commutative monoid, (ii) (M ;∨,∧, 0, 1) is a bounded lattice, and (iii) x y ≤ z ⇐⇒ x ≤ y → z, (iv) x (x → y) = x ∧ y, for each x, y, z ∈ M . In the sequel, by an R`-monoid we will mean a bounded commutative R`-monoid. (Note that bounded commutative R`-monoids are just bo...

It is known that the problem of determining consistency of a finite system of equations in a free group or a free monoid is decidable, but the corresponding problem for systems of equations in a free inverse monoid of rank at least two is undecidable. Any solution to a system of equations in a free inverse monoid induces a solution to the corresponding system of equations in the associated free...

It is well-known that many decision problems are undecidable in general for the class of all nite monoid-presentations. Here we consider the question of which of these problems remain undecidable even for very restricted classes of nite monoid-presentations. The restrictions we are interested in concern the number of generators admitted and the condition that each nite monoid-presentation consi...

We show that any normal algebraic monoid is an extension of an abelian variety by a normal affine algebraic monoid. This extends (and builds on) Chevalley’s structure theorem for algebraic groups.

Hybrid systems combine discrete and continuous dynamics. We introduce a semantics for such systems consisting of a coalgebra together with a monoid action. The coalgebra captures the (discrete) operations on a state space that can be used by a client (like in the semantics of ordinary (non-temporal) object-oriented systems). The monoid action captures the innuence of time on the state space, wh...

This paper gives decidable conditions for when a nitely generated subgroup of a free group is the fundamental group of a Sch utzenberger automaton corresponding to a monoid presentation of an inverse monoid. Also, generalizations are given to speciic types of inverse monoids as well as to monoids which are \nearly inverse." This result has applications to computing membership for inverse monoid...

It has been shown [6] that, within the McAlister inverse monoid [9], whose elements can be seen as overlapping one-dimensional tiles, the class of languages recognizable by finite monoids collapses compared with the class of languages definable in Monadic Second Order Logic (MSO). This paper aims at capturing the expressive power of the MSO definability of languages of tiles by means of a weake...

An atomic monoid M is called a length-factorial (or an other-half-factorial monoid) if for each non-invertible element x ? no two distinct factorizations of have the same length. The notion length-factoriality was introduced by Coykendall and Smith in 2011 as dual well-studied half-factoriality. They proved that setting integral domains, can be taken alternative definition unique factorization ...

We give a monoid presentation in terms of generators and defining relations for the partial analogue of the finite dual inverse symmetric monoid. AMS 2000 Mathematical Subject Classification 20M05, 68R15, 20M20.

In 1987 Squier defined the notion of finite derivation type for a finitely presented monoid. To do this, he associated a 2-complex to the presentation. The monoid then has finite derivation type if, modulo the action of the free monoid ring, the 1-dimensional homotopy of this complex is finitely generated. Cremanns and Otto showed that finite derivation type implies the homological finiteness c...