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.
