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

单词	AnnihilatorIsAnIdeal
释义	annihilator is an ideal The right annihilator of a right $R$ -module $M_{R}$ in $R$ is an ideal. Proof: By the distributive law for modules, it is easy to see that $\\operatorname{r.ann}(M_{R})$ is closed under addition and right multiplication.Now take $x\\in\\operatorname{r.ann}(M_{R})$ and $r\\in R$ . Take any $m\\in M_{R}$ . Then $mr\\in M_{R}$ , but then $(mr)x=0$ since $x\\in\\operatorname{r.ann}(M_{R})$ . So $m(rx)=0$ and $rx\\in\\operatorname{r.ann}(M_{R})$ . An equivalent result holds for left annihilators.
随便看	TableOfSubtractionUpTo12 table of subtraction up to 12 TableOfTheFirst100Primorials table of the first 100 primorials TableOfValuesForcosx table of values for ERROR(\symoperators)⁢c⁢o⁢s(x) table of values for ERROR(\symoperators)⁢s⁢i⁢n(x) table of values for ERROR(\symoperators)⁢t⁢a⁢n(x) TableOfValuesForsinx TableOfValuesFortanx TableOfValuesOfTheLiouvilleFunctionAndItsSummatoryFunction table of values of the Liouville function and its summatory function TableOfValuesOfTheMobiusFunctionAndTheMertensFunction table of values of the Möbius function and the Mertens function table of Wilson quotient for 0<n<41 TableOfWilsonQuotientFor0N41 Tabulation Examples TabulationExamples1 TacitExtension algorithm for modular exponentiation Aliasing aliasing ALineSegmentHasAtMostOneMidpoint a line segment has at most one midpoint AliquotSequence

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annihilator is an ideal