Local orders in Jordan algebras

JOURNAL OF ALGEBRA

卷:485

Article

Montaner, Fernando¹  Paniello, Irene² 

[1] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain

[2] Univ Publ Navarra, Dept Estadist & Invest Operat, Pamplona 31006, Spain

关键词: Jordan algebras;    Algebras of quotients;    Local algebras;    Socle;   

DOI  :  10.1016/j.jalgebra.2017.03.013

来源: Elsevier

【 摘 要 】

Making use of results on general algebras of quotients of Jordan algebras, we study a notion of local order based on the version for linear Jordan algebras of the ideas of Fountain and Gould [14] as adapted to the Jordan context by Fernandez-Lopez and Garcia-Rus in [7] In particular, we characterize the set of Lesieur-Croisot elements of a nondegenerate Jordan algebra as those elements of the Jordan algebra lying in the socle of its maximal algebra of quotients, and apply this relationship to extend to quadratic Jordan algebras the results of Fernandez-Lopez and Garcia-Rus on local orders in nondegenerate Jordan algebras satisfying the descending chain condition on principal inner ideals and not containing ideals which are nonartinian quadratic factors. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free