Band decompositions of semigroups
Mohan S. Putcha, Julian Weissglass · Proceedings of the American Mathematical Society · 1972
The existence of a band decomposition of a semigroup into semigroups having at most one idempotent and a group ideal whenever it has an idempotent is investigated. It is shown that S has such a band decomposition if and only if, for every c , d ∈ S 1 , a ∈ S d \in {S^1},a \in S , the idempotent multiples of cad and c a 2 d c{a^2}d coincide. The main result is used to characterize those semigroups which are bands of groups, extending a theorem of Clifford.