push-down theorem on class numbers

As in the parent (http://planetmath.org/ClassNumberDivisibilityInExtensions) entry, given a number field $K$ , the class number of $K$ is denoted by $h_{K}$ .

Theorem (Pushing-Down Theorem).

Let $E/F$ be a $p$ -extension of number fields and suppose that only one prime ideal of $F$ is ramified in $E$ and that this prime is totally ramified. Then $p|h_{E}$ implies $p|h_{F}$ .

References

Fröh A. Fröhlich, On a method for the determination of class number factors in number fields, Mathematika, 4 (1957), 113-121.
Iwas K. Iwasawa, A note on Class Numbers of Algebraic Number Fields, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 257-258.

单词	PushdownTheoremOnClassNumbers
释义	push-down theorem on class numbers As in the parent (http://planetmath.org/ClassNumberDivisibilityInExtensions) entry, given a number field $K$ , the class number of $K$ is denoted by $h_{K}$ . Theorem (Pushing-Down Theorem). Let $E/F$ be a $p$ -extension of number fields and suppose that only one prime ideal of $F$ is ramified in $E$ and that this prime is totally ramified. Then $p\|h_{E}$ implies $p\|h_{F}$ . References Fröh A. Fröhlich, On a method for the determination of class number factors in number fields, Mathematika, 4 (1957), 113-121. Iwas K. Iwasawa, A note on Class Numbers of Algebraic Number Fields, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 257-258.
随便看	subbasis Subbundle subbundle SubcoalgebrasAndCoideals subcoalgebras and coideals Subcommutative subcommutative SubdifferentiableMapping subdifferentiable mapping SubdirectlyIrreducibleRing subdirectly irreducible ring SubdirectProductOfAlgebraicSystems subdirect product of algebraic systems SubdirectProductOfGroups subdirect product of groups SubdirectProductOfRings subdirect product of rings Subdivision subdivision Subfield subfield SubfieldCriterion subfield criterion Subformula subformula