algebra Algebra () is one of the areas of mathematics, 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 mathem ...

, a Malcev-admissible algebra, introduced by , is a (possibly non-associative)

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 algebras.

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 Progress is the movement towards a refined, improved, or otherwise desired state. In the context of progressivism, it refers to the proposition that advancements in technology, science, and social organization have resulted, and by extension wi ...

, 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 (partic ...

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

See also

References