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Register a new userOn the question of embedding a semigroup into an idempotent generated one
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Luis Oliveira
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In this paper we present a new embedding of a semigroup into a semiband (idempotent-generated semigroup) of depth 4 (every element is the product of 4 idempotents) using a semidirect product construction. Our embedding does not assume that S is a monoid (although it assumes a weaker condition), and works also for (non-monoid) regular semigroups. In fact, this semidirect product is particularly useful for regular semigroups since we can defined another embedding for these semigroups into a smaller semiband of depth 2. We shall then compare our construction with other known embeddings, and we shall see that some properties of S are preserved by our embedding.
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We show that every periodic element of the free idempotent generated semigroup on an arbitrary biordered set belongs to a subgroup of the semigroup.
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