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Representation and structure
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a'ea a'ha a'xa According to Lemma analogous analogous computations aV(a b'eb band of idempotents congruence classes contains an idempotent Conversely Corollary 3.4 denote the set direct product e p f E-regular equivalence relation exists fl V(b follows from Lemma Green's relations Hall hence homomorphic image hypothesis identity relation imbedded inverse semigroup isomorphism least group congruence least inverse congruence Lemma l.2 maximum idempotent-separating congruence Meakin Moreover notation obtain Obviously one-to-one P-class P-related partial transformation preceding lemma Proof properties prove R-class rectangular band regular element regular semigroup regular subsemigroup Schein 22 semigroup and a,b semigroup of transformations semilattice set of idempotents set X written Similar computations similarly structure theorem Suppose theorem for orthodox Theorem l.9 transformation semigroups V(fa V(fb V(xe whence written as operators x a y x s/V xexex xV(x