Rees quotients of numerical semigroups

Growth of Finitely Presented Rees Quotients of Free Inverse Semigroups

We prove that a finitely presented Rees quotient of a free inverse semigroup has polynomial growth if and only if it has bounded height. This occurs if and only if the set of nonzero reduced words has bounded Shirshov height and all nonzero reduced but not cyclically reduced words are nilpotent. This occurs also if and only if the set of nonzero geodesic words have bounded Shirshov height. We a...

Function spaces of Rees matrix semigroups

We characterize function spaces of Rees matrixsemigroups. Then we study these spaces by using the topologicaltensor product technique.

Growth of Rees Quotients of Free inverse Semigroups Defined by Small numbers of Relators

We study the asymptotic behaviour of a finitely presented Rees quotient S = Inv〈A | ci = 0 (i = 1, . . . , k) 〉 of a free inverse semigroup over a finite alphabet A. It is shown that if the semigroup S has polynomial growth then S is monogenic (with zero) or k ≥ 3. The three relator case is fully characterised, yielding a sequence of two-generated three-relator semigroups whose Gelfand-Kirillov...

Automatic Rees Matrix Semigroups

We consider the preservation of the properties of automaticity and prefix-automaticity in Rees matrix semigroups over semigroupoids and small categories. Some of our results are new or improve upon existing results in the single-object case of Rees matrix semigroups over semigroups.

The Uniform Word Problem for Groups and Finite Rees Quotients of E-unitary Inverse Semigroups