Narrow Results

The objective of this paper is to document that the pseudovariety equation $PX=Com\ast D$ admits a solution $U$. This solution $U$ is a pseudovariety raised up by Almeida in his book on finite semigroups and universal algebra as a prospective candidate for such a solution. This result achieved in the present paper resolves an open problem posed by Almeida in his book a long time ago.