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A multiplication of e-varieties of regular -solid semigroups by inverse semigroup varieties is described both semantically and syntactically. The associativity of the multiplication is also proved.
We define semantically a partial multiplication on the lattice of all e–varieties of regular semigroups. In the case that the first factor is an e–variety of orthodox semigroups we describe our multiplication syntactically in terms of biinvariant congruences.
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