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- Minkowski's_bound abstract "In algebraic number theory, Minkowski's bound gives an upper bound of the norm of ideals to be checked in order to determine the class number of a number field K. It is named for the mathematician Hermann Minkowski.Let D be the discriminant of the field, n be the degree of K over , and be the number of complex embeddings where is the number of real embeddings. Then every class in the ideal class group of K contains an integral ideal of norm not exceeding Minkowski's boundMinkowski's constant for the field K is this bound MK.Since the number of integral ideals of given norm is finite, the finiteness of the class number is an immediate consequence, and further, the ideal class group is generated by the prime ideals of norm at most MK.The result is a consequence of Minkowski's theorem. Minkowski's bound may be used to derive a lower bound for the discriminant of a field K given n, r1 and r2. Since an integral ideal has norm at least one, we have 1 ≤ MK, so thatFor n at least 2, it is easy to show that the lower bound is greater than 1, so we obtain Minkowski's Theorem, that the discriminant of every number field, other than Q, is non-trivial. This implies that the field of rational numbers has no unramified extension.".
- Minkowski's_bound wikiPageExternalLink the-minkowski-bound.
- Minkowski's_bound wikiPageExternalLink ant.pdf.
- Minkowski's_bound wikiPageID "8491791".
- Minkowski's_bound wikiPageRevisionID "527815818".
- Minkowski's_bound hasPhotoCollection Minkowski's_bound.
- Minkowski's_bound id "6822".
- Minkowski's_bound title "Using Minkowski's Constant To Find A Class Number".
- Minkowski's_bound subject Category:Algebraic_number_theory.
- Minkowski's_bound comment "In algebraic number theory, Minkowski's bound gives an upper bound of the norm of ideals to be checked in order to determine the class number of a number field K. It is named for the mathematician Hermann Minkowski.Let D be the discriminant of the field, n be the degree of K over , and be the number of complex embeddings where is the number of real embeddings.".
- Minkowski's_bound label "Minkowski's bound".
- Minkowski's_bound sameAs m.0275czw.
- Minkowski's_bound sameAs Q6867845.
- Minkowski's_bound sameAs Q6867845.
- Minkowski's_bound wasDerivedFrom Minkowski's_bound?oldid=527815818.
- Minkowski's_bound isPrimaryTopicOf Minkowski's_bound.