Semigroups through semilattices
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.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
Carruth, J., & Lawson, J. (1970). Semigroups through semilattices. Transactions of the American Mathematical Society, 152 (2), 597-608. https://doi.org/10.1090/S0002-9947-1970-0268316-5