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单词 TranslationAutomorphismOfAPolynomialRing
释义

translation automorphism of a polynomial ring


Let R be a commutative ring, let R[X] be the polynomial ring over R, and let a be an element of R. Then we can define a homomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath τa of R[X] by constructing the evaluation homomorphism from R[X] to R[X] taking rR to itself and taking X to X+a.

To see that τa is an automorphismMathworldPlanetmath, observe that τ-aτa is the identityPlanetmathPlanetmath on RR[X] and takes X to X, so by the uniqueness of the evaluation homomorphism, τ-aτa is the identity.

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更新时间:2025/5/4 17:51:25