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- Tensor_product_of_fields abstract "In abstract algebra, the theory of fields 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).If K and L do not have isomorphic prime fields, or in other words they have different characteristics, they have no possibility of being common subfields of a field M. Correspondingly their tensor product will in that case be the trivial ring (collapse of the construction to nothing of interest).".
- Tensor_product_of_fields wikiPageExternalLink ant.pdf.
- Tensor_product_of_fields wikiPageExternalLink what-does-linearly-disjoint-mean-for-abstract-field-extensions.
- Tensor_product_of_fields wikiPageExternalLink ANT.pdf.
- Tensor_product_of_fields wikiPageID "372240".
- Tensor_product_of_fields wikiPageLength "9559".
- Tensor_product_of_fields wikiPageOutDegree "46".
- Tensor_product_of_fields wikiPageRevisionID "694286539".
- Tensor_product_of_fields wikiPageWikiLink A_priori_and_a_posteriori.
- Tensor_product_of_fields wikiPageWikiLink Abstract_algebra.
- Tensor_product_of_fields wikiPageWikiLink Algebra_over_a_field.
- Tensor_product_of_fields wikiPageWikiLink Algebraic_number_theory.
- Tensor_product_of_fields wikiPageWikiLink Artinian_ring.
- Tensor_product_of_fields wikiPageWikiLink Bijection.
- Tensor_product_of_fields wikiPageWikiLink Category:Field_theory.
- Tensor_product_of_fields wikiPageWikiLink Change_of_rings.
- Tensor_product_of_fields wikiPageWikiLink Characteristic_(algebra).
- Tensor_product_of_fields wikiPageWikiLink Cyclotomic_field.
- Tensor_product_of_fields wikiPageWikiLink Direct_product.
- Tensor_product_of_fields wikiPageWikiLink Field_(mathematics).
- Tensor_product_of_fields wikiPageWikiLink Field_extension.
- Tensor_product_of_fields wikiPageWikiLink Field_of_fractions.
- Tensor_product_of_fields wikiPageWikiLink Galois_theory.
- Tensor_product_of_fields wikiPageWikiLink Grothendiecks_Galois_theory.
- Tensor_product_of_fields wikiPageWikiLink Injective_function.
- Tensor_product_of_fields wikiPageWikiLink Integral_domain.
- Tensor_product_of_fields wikiPageWikiLink Linearly_disjoint.
- Tensor_product_of_fields wikiPageWikiLink Nilradical_of_a_ring.
- Tensor_product_of_fields wikiPageWikiLink P-adic_number.
- Tensor_product_of_fields wikiPageWikiLink Prime_ideal.
- Tensor_product_of_fields wikiPageWikiLink Prime_power.
- Tensor_product_of_fields wikiPageWikiLink Purely_inseparable_extension.
- Tensor_product_of_fields wikiPageWikiLink Radical_of_a_ring.
- Tensor_product_of_fields wikiPageWikiLink Ramification_(mathematics).
- Tensor_product_of_fields wikiPageWikiLink Rational_function.
- Tensor_product_of_fields wikiPageWikiLink Ring_(mathematics).
- Tensor_product_of_fields wikiPageWikiLink Root_of_unity.
- Tensor_product_of_fields wikiPageWikiLink Separable_extension.
- Tensor_product_of_fields wikiPageWikiLink Separable_polynomial.
- Tensor_product_of_fields wikiPageWikiLink Splitting_field.
- Tensor_product_of_fields wikiPageWikiLink Springer_Science+Business_Media.
- Tensor_product_of_fields wikiPageWikiLink Tensor_field.
- Tensor_product_of_fields wikiPageWikiLink Tensor_product.
- Tensor_product_of_fields wikiPageWikiLink Tensor_product_of_algebras.
- Tensor_product_of_fields wikiPageWikiLink Totally_real_number_field.
- Tensor_product_of_fields wikiPageWikiLink Tower_of_fields.
- Tensor_product_of_fields wikiPageWikiLink Up_to.
- Tensor_product_of_fields wikiPageWikiLink Vector_space.
- Tensor_product_of_fields wikiPageWikiLink Zero_ring.
- Tensor_product_of_fields wikiPageWikiLinkText "Tensor product of fields".
- Tensor_product_of_fields wikiPageWikiLinkText "tensor product algebra".
- Tensor_product_of_fields wikiPageWikiLinkText "tensor product of fields".
- Tensor_product_of_fields wikiPageWikiLinkText "tensor product".
- Tensor_product_of_fields id "C/c024310".
- Tensor_product_of_fields title "Compositum of field extensions".
- Tensor_product_of_fields wikiPageUsesTemplate Template:Citation.
- Tensor_product_of_fields wikiPageUsesTemplate Template:Distinguish2.
- Tensor_product_of_fields wikiPageUsesTemplate Template:Reflist.
- Tensor_product_of_fields wikiPageUsesTemplate Template:Springer.
- Tensor_product_of_fields subject Category:Field_theory.
- Tensor_product_of_fields type Thing.
- Tensor_product_of_fields comment "In abstract algebra, the theory of fields lacks a direct product: the direct product of two fields, considered as a ring is never itself a field.".
- Tensor_product_of_fields label "Tensor product of fields".
- Tensor_product_of_fields differentFrom Tensor_field.
- Tensor_product_of_fields sameAs Q340145.
- Tensor_product_of_fields sameAs Lineare_Disjunktheit.
- Tensor_product_of_fields sameAs Compositum.
- Tensor_product_of_fields sameAs 体のテンソル積.
- Tensor_product_of_fields sameAs Produto_tensorial_de_corpos.
- Tensor_product_of_fields sameAs m.020lf3.
- Tensor_product_of_fields sameAs Q340145.
- Tensor_product_of_fields wasDerivedFrom Tensor_product_of_fields?oldid=694286539.
- Tensor_product_of_fields isPrimaryTopicOf Tensor_product_of_fields.