Abstract
A semigroup endowed with a unary operation satisfying the identitiesis a completely regular semigroup. In several recent papers devoted to the study of the lattice of subvarieties of the variety of completely regular semigroups, various results have been obtained which decompose special intervals in into either direct products or subdirect products. Petrich [14], Hall and Jones [6] and Rasin [20] have shown that certain intervals of the form , where is the trivial variety and are subdirect products of and Pastijn and Trotter [13] show that certain intervals of the form are direct products of the intervals and The main objective of this paper is to develop an appropriate lattice theoretic framework for these representations.
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