Vol. 15, No. 4, 1965

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Generalized character semigroups: The Schwarz decomposition

You-Feng Lin

Vol. 15 (1965), No. 4, 1307–1312

The author’s résumé: A structure theorem due to Š. Schwarz asserts that if S is a finite abelian or a compact abelian semigroup admitting relative inverses, than the character semigroup of S is decomposed into a disjoint union of character groups of certain maximal subgroups of S. In this note, among other things, we generalize this Schwarz Decomposition Theorem to a broader class of semigroups, the so-called pseudo-invertible semigroups. We also relax the range of the characters from the semigroup of complex numbers to a more general semigroup.

Mathematical Subject Classification
Primary: 20.90
Received: 27 August 1964
Published: 1 December 1965
You-Feng Lin