Nilpotent and idempotent elements of subsemirings of the endomorphism semiring of an infinite chain

Autor:	Ivan Trendafilov, Dimitrinka Vladeva
Rok vydání:	2019
Předmět:	Equivalence class (music) Pure mathematics Nilpotent Endomorphism Ideal (set theory) Chain (algebraic topology) Mathematics::General Mathematics Mathematics::Rings and Algebras Idempotence Equivalence relation Computer Science::Formal Languages and Automata Theory Semiring Mathematics
Zdroj:	PROCEEDINGS OF THE 45TH INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’19).
ISSN:	0094-243X
DOI:	10.1063/1.5133606
Popis:	Idempotent and nilpotent elements are important in the structure of semigroups and semirings. In this article, we obtain some results of nilpotent endomorphisms of an infinite chain which applies to (multiplicatively) idempotents of the endomorphism semiring of a finite chain as well. 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 and roots of the idempotent is proposed. In our main result we prove that such equivalence class is a semiring and find his order.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7381f056177e6e18b8630fca4b189452 https://doi.org/10.1063/1.5133606 Zobrazit plný text záznamu