Tensor product of fields
Ring produced from two fields / From Wikipedia, the free encyclopedia
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For other uses, see Tensor product (disambiguation).
Not to be confused with Tensor field.
In mathematics, the tensor product of two fields is their tensor product as algebras over a common subfield. If no subfield is explicitly specified, the two fields must have the same characteristic and the common subfield is their prime subfield.
This article reads like a textbook. (August 2021) |
The tensor product of two fields is sometimes a field, and often a direct product of fields; In some cases, it can contain non-zero nilpotent elements.
The tensor product of two fields expresses in a single structure the different way to embed the two fields in a common extension field.