algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

, a Malcev-admissible algebra, introduced by , is a (possibly

non-associative In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement ...

)

that becomes a

Malcev algebra In mathematics, a Malcev algebra (or Maltsev algebra or Moufang– Lie algebra) over a field is a nonassociative algebra that is antisymmetric, so that :xy = -yx and satisfies the Malcev identity :(xy)(xz) = ((xy)z)x + ((yz)x)x + ((zx)x)y. Th ...

under the bracket 'a'', ''b''= ''ab'' − ''ba''. Examples include

alternative algebra In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have *x(xy) = (xx)y *(yx)x = y(xx) for all ''x'' and ''y'' in the algebra. Every associative algebra is ...

s, Malcev algebras and

Lie-admissible algebra In algebra, a Lie-admissible algebra, introduced by , is a (possibly non-associative) algebra that becomes a Lie algebra under the bracket 'a'', ''b''= ''ab'' − ''ba''. Examples include associative algebras, Lie algebras, and Okubo algebr ...

References

* * * *{{citation , last=Myung , first=Hyo Chul , year=1986 , title=Malcev-admissible algebras , url=https://books.google.com/books?id=PBvvAAAAMAAJ , series= Progress in Mathematics , volume=64 , publisher=

Birkhäuser Boston Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields: * Springer continues to publish science (parti ...

, place=Boston, MA , isbn= 0-8176-3345-6 , mr=0885089 , doi=10.1007/978-1-4899-6661-2 Non-associative algebra

See also

References