Abstract
Here, we have considered two equivalence relations [Formula: see text] and [Formula: see text] that are congruences on regular orthogroups but not on completely regular semigroups, in general. The congruence openings [Formula: see text] and [Formula: see text] of [Formula: see text] and [Formula: see text], respectively, induce new subvarieties [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for every [Formula: see text]; and are such that [Formula: see text] and [Formula: see text]. The decompositions of an arbitrary completely regular semigroup which are presented here generalize several spined product decompositions for particular classes of completely regular semigroups already given by several authors [M. Petrich and N. R. Reilly, Completely Regular Semigroup (Wiley, New York, 1999)], and thus contributes to a unification of the theory.
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