Orthogonal sums of semigroups
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The purpose of this paper is to prove that every semigroup with the zero is an orthogonal sum of orthogonal indecomposable semigroups. We prove that the set of all 0-consistent ideals of an arbitrary semigroup with the zero forms a complete atomic Boolean algebra whose atoms are summands in the greatest orthogonal decomposition of this semigroup.
KeywordsBoolean Algebra Inverse Semigroup Regular Semigroup Complete Boolean Algebra Arbitrary Semigroup
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- S. Bogdanović and M. Ćirić,Primitive π-regular semigroups, Japan Academy. Proceedings, Vol. 68, Series A10 (1992), 334–337.Google Scholar
- M. Ćirić and S. Bogdanović,Semilattice decompositions of semigroups, to appear.Google Scholar
- A. H. Clifford and G. B. Preston,The Algebraic Theory of Semigroups, I, American Mathematical Society, 1961.Google Scholar
- A. H. Clifford and G. B. Preston,The Algebraic Theory of Semigroups, II, American Mathematical Society, 1967.Google Scholar
- Š. Schwarz,On semigroups having a kernel, Czechoslovak Mathematical Journal1 (76) (1951), 259–301 (in Russian).Google Scholar