Alternativity
(Redirected from Right alternative)
This article may be too technical for most readers to understand.(November 2021) |
This article relies largely or entirely on a single source. (May 2024) |
In abstract algebra, alternativity is a property of a binary operation. A magma G is said to be left alternative if for all and right alternative if for all A magma that is both left and right alternative is said to be alternative (flexible).[1]
Any associative magma (that is, a semigroup) is alternative. More generally, a magma in which every pair of elements generates an associative submagma must be alternative. The converse, however, is not true, in contrast to the situation in alternative algebras. In fact, an alternative magma need not even be power-associative: already the expression cannot be proven to be identical to expressions such as purely by alternativity.
See also
References
- ^ Phillips, J. D.; Stanovský, David (2010), "Automated theorem proving in quasigroup and loop theory" (PDF), AI Communications, 23 (2–3): 267–283, doi:10.3233/AIC-2010-0460, MR 2647941, Zbl 1204.68181.
Categories:
- Articles with short description
- Short description is different from Wikidata
- Wikipedia articles that are too technical from November 2021
- All articles that are too technical
- Articles needing additional references from May 2024
- All articles needing additional references
- Properties of binary operations
- All stub articles
- Algebra stubs