Structure of the semigroup of semigroup extensions
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- by R. O. Fulp and J. W. Stepp PDF
- Trans. Amer. Math. Soc. 158 (1971), 63-73 Request permission
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.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 158 (1971), 63-73
- MSC: Primary 22.05
- DOI: https://doi.org/10.1090/S0002-9947-1971-0277651-7
- MathSciNet review: 0277651