论文标题
Artin近似Banach空间
Artin approximation over Banach spaces
论文作者
论文摘要
我们举例说明，通常，对于接通性Banach代数而在收敛序列中，对于在一个领域的融合系列有效的通常ARTIN近似定理是正确的。特别是，我们构建了一个交换性整体Banach代数$ r $的示例，使得超过$ r $的正式功率系列在$ r $ $ r $的趋同电源系列中并不平坦。
We give examples showing that the usual Artin Approximation theorems valid for convergent series over a field are no longer true for convergent series over a commutative Banach algebra. In particular we construct an example of a commutative integral Banach algebra $R$ such that the ring of formal power series over $R$ is not flat over the ring of convergent power series over $R$.
