Isomorphism problem for semigroups with one defining relation (Q800484)

It is proved that there exists an algorithm which solves the word problem for semigroups given by one defining relation of the kind \(a=A\), when a is a letter. The main result is the following theorem. Let \(K\) be the class of semigroups which are given by one defining relation with nonvoid defining words. There exists an algorithm by the help of which we can decide for two arbitrary semigroups in \(K\) whether or not these are isomorphic.