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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Semigroups through semilattices


Authors: J. H. Carruth and Jimmie D. Lawson
Journal: Trans. Amer. Math. Soc. 152 (1970), 597-608
MSC: Primary 22.05
MathSciNet review: 0268316
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Abstract: 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$.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0268316-5
Keywords: Compact semigroup, compact semilattice, clan, irreducible semigroup, generalized hormos, universal object
Article copyright: © Copyright 1970 American Mathematical Society