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

单词	ProductOfLeftAndRightIdeal
释义	product of left and right ideal Let $\\mathfrak{a}$ and $\\mathfrak{b}$ be ideals of a ring $R$ . Denote by $\\mathfrak{ab}$ the subset of $R$ formed by all finite sums of products $a b$ with $a\\in\\mathfrak{a}$ and $b\\in\\mathfrak{b}$ . It is straightforward to verify the following facts: • If $\\mathfrak{a}$ is a left (http://planetmath.org/Ideal) and $\\mathfrak{b}$ a right ideal, $\\mathfrak{ab}$ is a two-sided ideal of $R$ . • If both $\\mathfrak{a}$ and $\\mathfrak{b}$ are two-sided ideals, then $\\mathfrak{ab}\\subseteq\\mathfrak{a}\\cap\\mathfrak{b}$ .
随便看	ProofOfTheBurnsideBasisTheorem proof of the Burnside basis theorem ProofOfTheCauchyRiemannEquations proof of the Cauchy-Riemann equations ProofOfTheConverseOfLagrangesTheoremForFiniteCyclicGroups proof of the converse of Lagrange’s theorem for finite cyclic groups ProofOfTheCorrespondenceBetweenEven2superperfectNumbersAndMersennePrimes proof of the correspondence between even 2-superperfect numbers and Mersenne primes ProofOfTheDebutTheorem ProofOfTheDeterminantConditionForASequenceOfVectors proof of the determinant condition for a sequence of vectors ProofOfTheDimensionTheoremForSubspaces proof of the dimension theorem for subspaces proof of the début theorem ProofOfTheExistenceOfTranscendentalNumbers 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

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product of left and right ideal