Peirce-evanescent baric identities
| Autor: | Richard Varro |
|---|---|
| Přispěvatelé: | Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Polynomial
Pure mathematics Algebra and Number Theory [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC] Mathematics::History and Overview 010102 general mathematics Null (mathematics) Spectrum (functional analysis) Field (mathematics) 01 natural sciences Identity (mathematics) 0103 physical sciences Mutation (knot theory) 010307 mathematical physics 0101 mathematics Algebraic number Commutative property ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Journal of Algebra Journal of Algebra, Elsevier, 2020, 564, pp.49-97. ⟨10.1016/j.jalgebra.2020.08.006⟩ |
| ISSN: | 0021-8693 1090-266X |
| DOI: | 10.1016/j.jalgebra.2020.08.006⟩ |
| Popis: | Peirce-evanescent baric identities are polynomial identities verified by baric algebras such that their Peirce polynomials are the null polynomial. In this paper procedures for constructing such homogeneous and non homogeneous identities are given. For this we define an algebraic system structure on the free commutative nonassociative algebra generated by a set T which provides for classes of baric algebras satisfying a given set of identities similar properties to those of the varieties of algebras. Rooted binary trees with labeled leaves are used to explain the Peirce polynomials. It is shown that the mutation algebras satisfy all Peirce-evanescent identities, it results from this that any part of the field K can be the Peirce spectrum of a K-algebra satisfying a Peirce-evanescent identity. We end by giving methods to obtain generators of homogeneous and non-homogeneous Peirce-evanescent identities that are applied in several univariate and multivariate cases. |
| Databáze: | OpenAIRE |
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