Grushko-like theorems for a class of finitely presented semigroups
Ann Yasuhara · Proceedings of the American Mathematical Society · 1974
An analogue of Grushko’s theorem and the unsolvability of the isomorphism problem hold for semigroups in the class of all finitely presented semigroups that have a presentation in which there is no defining relation of the form $1 \Leftrightarrow A$; this class is not recursive but is recursively enumerable.