Journal Title/Source
Quasigroups and Related Systems
Publication Date
2023
Volume
31
Page Numbers
241–259
Document Type
Journal Article
Department
Mathematics and Computer Science
Abstract
In the two subvarieties of commutative not necessarily associative rings, and 2-divisible not necessarily associative rings, we show that the sixty Bol-Moufang identities determine exactly five subvarieties in each case, and we completely determine all inclusions and necessary counterexamples. The historically important nonassociative rings of octonions and sedenions may be used as counterexamples in our classification. We utilize both associator and linear forms of each Bol-Moufang identity. The results are analogous to the classification of varieties of loops or quasigroups of Bol-Moufang type (Phillips, Vojtěchovský-2005)
Recommended Citation
Phillips, J.D., "Commutative and 2-Divisible Subvarieties of Rings of Bol-Moufang Type" (2023). Journal Articles. 513.
https://commons.nmu.edu/facwork_journalarticles/513