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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