Semigroups through semilattices

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Presented in this paper is a method of constructing a compact semi­group S from a compact semilattice X and a compact semigroup T having idempotents contained in X. The notions of semigroups (straight) through chains and (straight) through semilattices are introduced. It is shown that the notion of a semigroup through a chain is equivalent to that of a generalized hormos. Universal objects are obtained in several categories including the category of clans straight through a chain and the category of clans straight through a semilattice relative to a chain. An example is given of a nonabelian clan S with abelian set of idempotents E such that S is minimal (as a clan) about E. © 1970 American Mathematical Society.

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Transactions of the American Mathematical Society

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