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- W804390354 abstract "Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that <TEX>$K;{otimes}_F;L;=; N_1;{oplus}N_2;{oplus}{cdots}{oplus}N_k$</TEX> with corresponding primitive idempotents <TEX>$e_1,;e_2,{cdots},e_k$</TEX>, where Ni's are fields. Then G acts on <TEX>${e_1,;e_2,{cdots},e_k}$</TEX> transitively and <TEX>$Gal(N_1/K);{cong};{sigma;{in};G;/;{sigma}(e_1);=;e_1}$</TEX>. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = <TEX>$K;{otimes}_F;R$</TEX>, and suppose there are only finitely many prime ideals <TEX>$Q_1,;Q_2,{cdots},Q_k$</TEX> of T with <TEX>$Q_i;{cap};R;=;P$</TEX>. Then G acts transitively on <TEX>${Q_1,;Q_2,{cdots},Q_k},;and;Gal(qf(T/Q_1)/qf(R/P));{cong};{sigma{in};G/;{sigma}-(Q_1);=;Q_1}$</TEX> where qf(<TEX>$T/Q_1$</TEX>) is the quotient field of <TEX>$T/Q_1$</TEX>." @default.
- W804390354 created "2016-06-24" @default.
- W804390354 creator A5086543506 @default.
- W804390354 date "2005-10-01" @default.
- W804390354 modified "2023-10-18" @default.
- W804390354 title "AN ACTION OF A GALOIS GROUP ON A TENSOR PRODUCT" @default.
- W804390354 doi "https://doi.org/10.4134/ckms.2005.20.4.645" @default.
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