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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Structure of the semigroup of semigroup extensions


Authors: R. O. Fulp and J. W. Stepp
Journal: Trans. Amer. Math. Soc. 158 (1971), 63-73
MSC: Primary 22.05
MathSciNet review: 0277651
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Abstract: Let $ B$ denote a compact semigroup with identity and $ G$ a compact abelian group. Let $ \operatorname{Ext} (B,G)$ denote the semigroup of extensions of $ G$ by $ B$. We show that $ \operatorname{Ext} (B,G)$ is always a union of groups. We show that it is a semilattice whenever $ B$ is. In case $ B$ is also an abelian inverse semigroup with its subspace of idempotent elements totally disconnected, we obtain a determination of the maximal groups of a commutative version of $ \operatorname{Ext} (B,G)$ in terms of the extension functor of discrete abelian groups.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0277651-7
PII: S 0002-9947(1971)0277651-7
Keywords: Extension of compact semigroups, groups by semigroups, groups by semilattices, groups by inverse semigroups, character groups, inverse systems of groups
Article copyright: © Copyright 1971 American Mathematical Society