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- Title
Commutative and 2-divisible subvarieties of rings of Bol-Moufang type.
- Authors
Hemmila, Davin; Phillips, J. D.; Rowe, Daniel; White, Ron
- 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, Vojtechovský-2005).
- Subjects
NONASSOCIATIVE algebras; QUASIGROUPS; CAYLEY numbers (Algebra); ASSOCIATIVE rings; COMMUTATIVE rings
- Publication
Quasigroups & Related Systems, 2023, Vol 31, Issue 2, p241
- ISSN
1561-2848
- Publication type
Article
- DOI
10.56415/qrs.v31.19