Книга: Tensor Product of Fields: Mathematics, Field (mathematics), Abstract Algebra, Direct Product, Field Extension, Distributivity, Ordered Field, Finite Field, P-adic Number, Linear Algebra

High Quality Content by WIKIPEDIA articles! In mathematics, the theory of fields in abstract algebra lacks a direct product: the direct product of two fields, considered as a ring is never itself a field. On the other hand it is often required to 'join' two fields K and L, either in cases where K and L are given as subfields of a larger field M, or when K and L are both field extensions of a smaller field N (for example a prime field). The tensor product of fields is the best available construction on fields with which to discuss all the phenomena arising. As a ring, it is sometimes a field, and often a direct product of fields it can, though, contain non-zero nilpotents (see radical of a ring).