2012/10/28 by Ivan Trendafilov, Trendafilov, Ivan, Dimitrinka Vladeva +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · Mathematics · #Chemical Synthesis and Analysis #Synthesis and properties of polymers #math.GR #math.RA #msc:06A05 #msc:16Y60 #msc:20M20 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1210.7405
15 pages, 1 figure
arxiv created 2012/10/28 · arxiv updated 2012/10/30
Idempotents yield much insight in the structure of finite semigroups and semirings. In this article, we obtain some results on (multiplicatively) idempotents of the endomorphism semiring of a finite chain. We prove that the set of all idempotents with certain fixed points is a semiring and find its order. We further show that this semiring is an ideal in a well known semiring. The construction of an equivalence relation such that any equivalence class contain just one idempotent is proposed. In our main result we prove that such equivalence class is a semiring and find his order. We prove that the set of all idempotents with certain jump points is a semiring.