Ordered Structures of Polynomials over Max-Plus Algebra

Autor: Yuanqing Xia, Yuegang Tao, Cailu Wang
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Symmetry
Volume 13
Issue 7
Symmetry, Vol 13, Iss 1137, p 1137 (2021)
ISSN: 2073-8994
DOI: 10.3390/sym13071137
Popis: The ordered structures of polynomial idempotent algebras over max-plus algebra are investigated in this paper. Based on the antisymmetry, the partial orders on the sets of formal polynomials and polynomial functions are introduced to generate two partially ordered idempotent algebras (POIAs). Based on the symmetry, the quotient POIA of formal polynomials is then obtained. The order structure relationships among these three POIAs are described: the POIA of polynomial functions and the POIA of formal polynomials are orderly homomorphic
the POIA of polynomial functions and the quotient POIA of formal polynomials are orderly isomorphic. By using the partial order on formal polynomials, an algebraic method is provided to determine the upper and lower bounds of an equivalence class in the quotient POIA of formal polynomials. The criterion for a formal polynomial to be the minimal element of an equivalence class is derived. Furthermore, it is proven that any equivalence class is either an uncountable set with cardinality of the continuum or a finite set with a single element.
Databáze: OpenAIRE
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