Closed ideals in \(C^\infty\) with the Duhamel product as multiplication (Q703651)

Let \((C^{\infty}, \circledast)\) denote the algebra of infinitely differentiable functions in \([0,1]\) with the Duhamel product \(\circledast\) as multiplication. Let \[ C_{0}^{(n)}= \{f \in C^{\infty}: f^{(i)}(0)=0, i=0,1,2,\dots,n\}\;(n=0,1,2,\dots), \] \[ C_{\lambda}= \{ f \in C^{\infty}: f(x)=0, x \in [0, {\lambda}] \}\;(0 < \lambda < 1). \] In the paper under review, the author proves that all closed ideals in \((C^{\infty}, \circledast)\) are of the form \(C_{0}^{(n)}(n=0,1,2,\dots)\) or of the form \(C_{\lambda}\) \((0 < \lambda <1)\).