Idempotents yield much insight in the structure of finite semigroups andsemirings. In this article, we obtain some results on (multiplicatively)idempotents of the endomorphism semiring of a finite chain. We prove that theset of all idempotents with certain fixed points is a semiring and find itsorder. We further show that this semiring is an ideal in a well known semiring.The construction of an equivalence relation such that any equivalence classcontain just one idempotent is proposed. In our main result we prove that suchequivalence class is a semiring and find his order. We prove that the set ofall idempotents with certain jump points is a semiring.
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