Tensor Product of Fields | Mathematics, Field (mathematics), Abstract Algebra, Direct Product, Field Extension, Distributivity, Ordered Field, Finite Field, P-adic Number, Linear Algebra. This item is unavailable.Tensor Product of Fields | Mathematics, Field (mathematics), Abstract Algebra, Direct Product, Field Extension, Distributivity, Ordered Field, Finite Field, P-adic Number, Linear Algebra

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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).

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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).