Tensor product of associative algebras
= Tensor product of associative algebras
{title2=$(a\otimes b)(c\otimes d)=ac\otimes bd$}
For two unital <associative algebras> over a <field> $k$, their <tensor product> carries the multiplication in the title, extended by <bilinearity>, with identity $1\otimes1$. Choosing a <basis> $(b_j)$ of the second factor gives the <basis of a module> $(1\otimes b_j)$ for the resulting left $A$-<module>; <dual basis> functionals recover the coefficients uniquely.