Facts about algebras involving bilinear maps and tensor products #
We move a few basic statements about algebras out of
in order to avoid importing
The multiplication in an algebra is a bilinear map.
A weaker version of this for semirings exists as
The multiplication on the left in an algebra is a linear map.
The multiplication on the right in an algebra is a linear map.
Simultaneous multiplication on the left and right is a linear map.
The multiplication map on an algebra, as an
R-linear map from
A ⊗[R] A to