arXiv subjects
Publications and source records attributed to Ivan Trendafilov.
We establish new results concerning endomorphisms of a finite chain if the cardinality of the image of such endomorphism is no more than some fixed number. The semiring of all such endomorphisms can be seen as a simplex whose vertices are the constant endomorphisms. We explore the properties of these simplices.
We investigate endomorphism semirings of a finite semilattice with one least element and one greatest element such that all the other elements form an antichain. We construct some new finite simple semirings. Keywords: endomorphism semiring, additively idempotent semiring, simple semiring, idempotent endomorphism, finite semilattice.
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.
The goal of this paper is to provide some basic structure information on derivations in finite semirings.