“IntegralityIsTransitive”的概念、定义、习题解题方法及翻译-数学辞典

单词	IntegralityIsTransitive
释义	integrality is transitive Let $C\\subset B\\subset A$ be rings. If $B$ is integral over $C$ and $A$ is integral over $B$ , then $A$ is integral over $C$ . Proof. Choose $u\\in A$ . Then $u^{n}+b_{1}u^{n-1}+\\cdots+b_{n}=0,b_{i}\\in B$ . Thus $C[b_{1},\\ldots,b_{n},u]$ is integral and thus module-finite over $C[b_{1},\\ldots,b_{n}]$ . Each $b_{i}$ is integral over $C$ , so $C[b_{1},\\ldots,b_{n}]$ is integral hence module-finite over $C$ . Thus $C[b_{1},\\ldots,b_{n},u]$ is module-finite, hence integral, over $C$ , so $u$ is integral over $C$ .
随便看	proof of the existence of transcendental numbers ProofOfTheFundamentalTheoremOfAlgebraLiouvillesTheorem proof of the fundamental theorem of algebra (Liouville’s theorem) ProofOfTheFundamentalTheoremOfCalculus proof of the fundamental theorem of calculus ProofOfTheJordanHolderDecompositionTheorem proof of the Jordan Hölder decomposition theorem ProofOfTheoremAboutCyclicSubspaces proof of theorem about cyclic subspaces ProofOfTheoremForNormalMatrices proof of theorem for normal matrices ProofOfTheoremOnEquivalentValuations proof of theorem on equivalent valuations ProofOfTheoremsInAdditivelyIndecomposable proof of theorems in additively indecomposable ProofOfThePowerRule proof of the power rule ProofOfTheRingOfIntegersOfANumberFieldIsFinitelyGeneratedOvermathbbZ proof of the ring of integers of a number field is finitely generated over ℤ ProofOfTheUniformizationTheorem proof of the uniformization theorem ProofOfTheWeakNullstellensatz proof of the weak Nullstellensatz ProofOfTheWellfoundedInductionPrinciple proof of the well-founded induction principle

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。

integrality is transitive