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

单词	RingfiniteIntegralExtensionsAreModulefinite
释义	ring-finite integral extensions are module-finite Theorem If $B$ is a subring of $A$ and $u_{1},\\ldots,u_{s}\\in A$ are integral over $B$ , then $B[u_{1},\\ldots,u_{s}]$ is module-finite over $B$ . Proof.If $s=1$ then $u^{n}+b_{1}u^{n-1}+\\cdots+b_{n}=0$ , so $\\{1,u,\\ldots,u^{n-1}\\}$ spans $B[u]$ over $B$ . If $s>1$ , use induction on $B\\subset B[u_{1}]\\subset B[u_{1},u_{2}]\\subset\\ldots\\subset B[u_{1},\\ldots,u_{%s}]$ and multiply the spanning sets together.
随便看	ExampleOfConformalMapping example of conformal mapping ExampleOfConstructionOfASchauderBasis example of construction of a Schauder basis ExampleOfContinuousBijectionsWhichAreNotHomeomorphisms example of continuous bijections which are not homeomorphisms ExampleOfContractiveSequence example of contractive sequence ExampleOfConvergingIncreasingSequence example of converging increasing sequence ExampleOfCountingTheorem example of counting theorem ExampleOfCramersRule example of Cramer’s rule ExampleOfCurvaturespaceCurve example of curvature (space curve) ExampleOfCylindricAlgebra example of cylindric algebra ExampleOfDefinableType example of definable type ExampleOfDeRhamCohomology example of de Rham cohomology ExampleOfDerivativeAsParameter example of derivative as parameter ExampleOfDifferentiableFunctionWhichIsNotContinuouslyDifferentiable

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。

ring-finite integral extensions are module-finite