Journal Title/Source

Journal of Algebra and its Applications

Publication Date

2024

Volume

23

Page Numbers

1-20

Document Type

Journal Article

Department

Mathematics and Computer Science

Abstract

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, Vojtěchovský2005) 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).

Keywords: nonassociative algebra, nonassociative rings, rings of Bol-Moufang type, Moufang rings, alternative rings, magma rings, tangent algebras to smooth loops

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