minimality of integral basis

The discriminant $\\Delta:=\\Delta(\\alpha_{1},\\,\\alpha_{2},\\,\\ldots,\\,\\alpha_{s})$ of the set $\\{\\alpha_{1},\\,\\alpha_{2},\\,\\ldots,\\,\\alpha_{s}\\}$ of integers of an algebraic number field $K$ is a rational integer. If this set is an integral basis of $K$ , then $|\\Delta|$ has the least possible (positive integer) value in the field $K$ , and conversely. The value $d=\\Delta$ is equal for all integral bases of $K$ , and it is called the discriminant or fundamental number of the field.

单词	MinimalityOfIntegralBasis
释义	minimality of integral basis The discriminant $\\Delta:=\\Delta(\\alpha_{1},\\,\\alpha_{2},\\,\\ldots,\\,\\alpha_{s})$ of the set $\\{\\alpha_{1},\\,\\alpha_{2},\\,\\ldots,\\,\\alpha_{s}\\}$ of integers of an algebraic number field $K$ is a rational integer. If this set is an integral basis of $K$ , then $\|\\Delta\|$ has the least possible (positive integer) value in the field $K$ , and conversely. The value $d=\\Delta$ is equal for all integral bases of $K$ , and it is called the discriminant or fundamental number of the field.
随便看	Kummer’s congruence Kummer’s lemma Kummer’s theorem KunihikoKodaira Kunihiko Kodaira KunnethTheorem Kunneth theorem KupkaSmale Kupka-Smale KupkaSmaleTheorem Kupka-Smale theorem KuratowskiClosurecomplementTheorem Kuratowski closure-complement theorem KuratowskisEmbeddingTheorem KuratowskisLemma KuratowskisTheorem Kuratowski’s embedding theorem Kuratowski’s lemma Kuratowski’s theorem KurodaNormalForm Kuroda normal form KuroshOreTheorem Kurosh-Ore theorem KurtHeegner Kurt Heegner