Peirce-evanescent baric identities

JOURNAL OF ALGEBRA

卷:564

Article

Varro, Richard¹ 

[1] Univ Montpellier, Inst Montpellierain Alexander Grothendieck, CNRS, Pl Eugene Bataillon, F-35095 Montpellier, France

关键词: Baric algebras;    Polynomial identities;    Algebraic systems;    Variety of algebraic systems;    T-ideal;    Labeled rooted binary trees;    Altitude of a polynomial;    Peirce polynomial;    Mutation algebras;   

DOI  :  10.1016/j.jalgebra.2020.08.006

来源: Elsevier

【 摘 要 】

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. (C) 2020 Published by Elsevier Inc.

【 授权许可】

Free