# NonAssociativeAlgebra RΒΆ

NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms `r*`(a*b) = (r*a)`*b` = a*(`r*b`)

0: %

from AbelianMonoid

*: (%, %) -> %

from Magma

*: (%, R) -> %

from RightModule R

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

antiCommutator: (%, %) -> %
associator: (%, %, %) -> %
coerce: % -> OutputForm
commutator: (%, %) -> %
latex: % -> String

from SetCategory

leftPower: (%, PositiveInteger) -> %

from Magma

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> %

`plenaryPower(a, n)` is recursively defined to be `plenaryPower(a, n-1)*plenaryPower(a, n-1)` for `n>1` and `a` for `n=1`.

rightPower: (%, PositiveInteger) -> %

from Magma

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(R, R)

CancellationAbelianMonoid

Magma

NonAssociativeRng

NonAssociativeSemiRng

SetCategory