The structure of solid binary algebras
This paper gives an account of the structure of so-called solid binary algebras which are an abstract characterisation of the idempotent structure of a completely regular semigroup (a semigroup which is a union of groups). The main result is a structure theorem for solid binary algebras in terms of semilattices and rectangular bands. It is an analogue of the classical structure theorem for bands due to Petrich. It is shown that any solid binary algebra generated by two elements is a band, but an example shows that this does not hold for three or more generators. Finally it is proved that the free solid binary algebra can be embedded in a free completely regular semigroup, thus allowing the solution of the word problem for free solid binary algebras.
scientific article; zbMATH DE number 920793