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Differential Simplicity in Polynomial Rings and Algebraic Independence of Power Series |
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| Authors: | Brumatti Paulo; Lequain Yves; Levcovitz Daniel |
| Institution: | IMECC, Universidade Estadual de Campinas 13801-970 Campinas, SP, Brazil brumatti{at}ime.unicamp.br Instituto de Matemática Pura e Aplicada Estrada Dona Castorina 110, Jardim Botânico, 22460-320 Rio de Janeiro, RJ, Brazil ylequain{at}impa.br Instituto de Ciências Matemáticas e de Computação USP-SC, Av. Dr Carlos Botelho, 1465, 13560-970 São Carlos, SP, Brazil lev{at}icmc.usp.br |
| Abstract: | Let k be a field of characteristic zero, f(X,Y), g(X,Y) kX,Y],g(X,Y)  (X,Y) and d:=g(X,Y) /X + f(X,Y)/Y. A connection is establishedbetween the d-simplicity of the local ring kX,Y](X,Y) and thetranscendency of the solution in tkt]] of the algebraic differentialequation g(t,y(t))·(/t)y(t)+f(t,y(t)). This connectionis used to obtain some interesting results in the theory ofthe formal power series and to construct new examples of differentiallysimple rings. |
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