A decision problem for varieties of commutative semigroups

Varieties of Commutative Semigroups

In this paper, we describe all equational theories of commutative semigroups in terms of certain well-quasi-orderings on the set of finite sequences of nonnegative integers. This description yields many old and new results on varieties of commutative semigroups. In particular, we obtain also a description of the lattice of varieties of commutative semigroups, and we give an explicit uniform sol...

Free Partially Commutative Semigroups in Band Varieties 3

The Conjugacy Problem for Hnn Groups and the Word Problem for Commutative Semigroups

We show how a positive solution to the word problem for finitely generated commutative semigroups leads to a positive solution to the conjugacy problem for a class of HNN groups. Here we answer a question of Professor Wilhelm Magnus concerning the solvability of the conjugacy problem of the groups VA discussed in [1]. These groups are given by (I) <tf„ . . . , ak, b; af^b"'ax = bq\ . . . , ak^b...

Totally Ordered Commutative Semigroups

Let 5( + , < ) be a system consisting of a set S endowed with an associative binary operation + and a total ( = linear = simple) order relation < . The composition + and the relation < may be connected by either or both of the following conditions. MC (Monotone Condition). If a and b are elements of 5 such that ax+y ...

Bases for commutative semigroups and groups

A base for a commutative semigroup (S,+) is an indexed set 〈xt〉t∈A in S such that each element x ∈ S is uniquely representable as ∑t∈F xt where F is a finite subset of A and, if S has an identity 0, then 0 = ∑n∈ xt . We investigate those commutative semigroups or groups which have a base. We obtain the surprising result that Q has a base. More generally, we show that an abelian group has a base...