Editing Tensor product of fields (section)

==The tensor product as ring==

To get a general theory, one needs to consider a [[ring (mathematics)|ring]] structure on <math>K \otimes_N L</math>. One can define the product <math>(a\otimes b)(c\otimes d)</math> to be <math> ac \otimes bd</math> (see [[Tensor product of algebras]]). This formula is multilinear over ''N'' in each variable; and so defines a ring structure on the tensor product, making <math>K \otimes_N L</math> into a [[commutative algebra (structure)|commutative ''N''-algebra]], called the '''tensor product of fields'''.