Alternativity
This article may be too technical for most readers to understand.(November 2021) |
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.
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:
- Properties of binary operations
- Algebra stubs