Taylor series and divisibility |
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| Authors: | A. A. Evyatar O. E. Villamayor |
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| Affiliation: | 1. Department of Mathematics, Technion — Israel Institute of Technology, Haifa, Israel
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| Abstract: | LetA be an augmentedK-algebra; defineT:A →A ?k kA byT(a)=1?a ?a?1,a ∈A. We prove, under some conditions, thatg is in the subalgebraK[f] ofA generated byf if and only ifT(g) is in the principal ideal generated byT(f) inA?k kA. WhenA=K[[X]],T(f) is a multiple ofT(X) if and only iff belongs to the ringL obtained by localizingK[X] at (X). |
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