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

单词	EveryAlgebraicallyClosedFieldIsPerfect
释义	every algebraically closed field is perfect Proposition 1. Every algebraically closed field is perfect Proof. Let $K$ be an algebraically closed field of prime characteristic $p$ . Take $a\\in K$ . Then the polynomial $X^{p}-a$ admits a zero in $K$ . It follows that $a$ admits a $p$ th root in $K$ . Since $a$ is arbitrary we have proved that the field $K$ is perfect.∎
随便看	ProofOfGeneralizationOfTheParallelogramLaw proof of generalization of the parallelogram law ProofOfGeneralizedLeibnizRule proof of generalized Leibniz rule ProofOfGeneralizedRuizsIdentity proof of generalized Ruiz’s identity ProofOfGeneralMeansInequality proof of general means inequality ProofOfGeneralStokesTheorem proof of general Stokes theorem ProofOfGoursatsTheorem proof of Goursat’s theorem ProofOfGramSchmidtOrthogonalizationProcedure proof of Gram-Schmidt orthogonalization procedure ProofOfGreensTheorem proof of Green’s theorem ProofOfGronwallsLemma proof of Gronwall’s lemma ProofOfGrowthOfExponentialFunction proof of growth of exponential function ProofOfHadamardsInequality ProofOfHadamardThreecircleTheorem proof of Hadamard three-circle theorem proof of Hadamard’s inequality ProofOfHadwigerFinslerInequality

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。

every algebraically closed field is perfect