“UnityOfSubring”的概念、定义、习题解题方法及翻译-数学辞典

单词	UnityOfSubring
释义	unity of subring Theorem. Let $S$ be a proper subring of the ring $R$ . If $S$ has a non-zero unity $u$ which is not unity of $R$ , then $u$ is a zero divisor of $R$ . Proof. Because $u$ is not unity of $R$ , there exists an element $r$ of $R$ such that $ru\eq r$ . Then we have $(ru)u=r(uu)=ru$ , which implies that $0=(ru)u-ru=(ru-r)\\cdot u$ . Since neither $ru-r$ nor $u$ is 0, the element $u$ is a zero divisor in $R$ .
随便看	a nontrivial normal subgroup of a finite p-group G and the center of G have nontrivial intersection AnosovDiffeomorphism Anosov diffeomorphism AnotherDefinitionOfCofinality another definition of cofinality AnotherExampleOfDiracSequence another example of Dirac sequence AnotherProofOfBernoullisInequality another proof of Bernoulli’s inequality AnotherProofOfCardinalityOfTheRationals another proof of cardinality of the rationals AnotherProofOfDinisTheorem another proof of Dini’s theorem AnotherProofOfJensensInequality another proof of Jensen’s inequality AnotherProofOfPigeonholePrinciple another proof of pigeonhole principle AnotherProofOfRanknullityTheorem another proof of rank-nullity theorem AnotherProofOfTheNonexistenceOfAContinuousFunctionThatSwitchesTheRationalAndTheIrrationalNumbers another proof of the non-existence of a continuous function that switches the rational and the irrational numbers AnotherProofOfYoungInequality another proof of Young inequality AnotherProofThatANumberIsPoliteIffItIsPositiveAndNotAPositivePowerOf2 another proof that a number is polite iff it is positive and not a positive power of 2

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。

unity of subring

Theorem.