Differential Simplicity in Polynomial Rings and Algebraic Independence of Power Series
Differential Simplicity in Polynomial Rings and Algebraic Independence of Power Series
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DOI：
10.1112/s0024610703004708
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发表时间：
2003-12
期刊：
影响因子：
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通讯作者：
P. Brumatti;Y. Lequain;D. Levcovitz
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文献类型：
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作者：
P. Brumatti;Y. Lequain;D. Levcovitz
设k是特征为零的域，f（X，Y），g（X，Y）∈k[X，Y]，g（X，Y）<$（X，Y）且d：=g（X，Y）δ/δX + f（X，Y）δ/δY.建立了局部环k[X，Y]（X，Y）的d-单性与代数微分方程g（t，y（t））·（δ/δt）y（t）+f（t，y（t））的解在tk[[t]]中的超越性之间的联系。这种连接是用来获得一些有趣的结果，在理论的正式幂级数和建设新的例子，差分简单的环。
Let k be a field of characteristic zero, f(X,Y), g(X,Y)∈k[X,Y], g(X,Y) ∉ (X,Y) and d:=g(X,Y)δ/δX + f(X,Y)δ/δY. A connection is established between the d‐simplicity of the local ring k[X,Y](X,Y) and the transcendency of the solution in tk[[t]] of the algebraic differential equation g(t,y(t))·(δ/δt)y(t)+f(t,y(t)). This connection is used to obtain some interesting results in the theory of the formal power series and to construct new examples of differentially simple rings.