The varieties of rings of Bol-Moufang type

被引：0

作者：

Hemmila, Davin ^{[1
]}

Phillips, J. D. ^{[1
]}

Rowe, Daniel ^{[1
]}

White, Ron ^{[2
]}

机构：

[1] Northern Michigan Univ, Dept Math & Comp Sci, 1401 Presque Isle Ave, Marquette, MI 49855 USA

[2] Southern Illinois Univ, Sch Math & Stat Sci, 1263 Lincoln Dr, Carbondale, IL 62901 USA

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2024年 / 23卷 / 11期

关键词：

Nonassociative algebra; nonassociative rings; rings of Bol-Moufang type; Moufang rings; alternative rings; magma rings; tangent algebras to smooth loops; IDENTITIES;

D O I：

10.1142/S0219498824501779

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the variety of not necessarily associative rings, we show that the sixty Bol-Moufang identities determine exactly thirteen subvarieties, and we determine all inclusions and necessary counterexamples. We make use of the concepts of magma rings and linear identities. The result is analogous to the classification of varieties of loops or quasigroups of Bol-Moufang type (Phillips, Vojtechovsky-2005) and was motivated by the study of tangent algebras to smooth loops of Bol-Moufang type (Mal'cev-1955, Sagle-1961, Nagy 1992, Bremner, Madariaga-2014).

引用

页数：18

共 50 条

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