Abstract
Suppose that an ideal $J$ of $C^\infty$ functions on an open subset of $\mathbf{R}^2$ is a Łojasiewicz ideal. We describe the set of $C^\infty$ functions vanishing on the zeros of $J$ explicitly using $J$ in an open neighborhood of each point in zeros of $J$, it can be obtained by taking real radical and closure starting from $J$ repeatedly for a finite number of times. This gives an another affirmative answer to Bochnak's conjecture in dimension 2, which is first done by Risler.
Acknowledgment
The author would like to express my sincere gratitude to Professor Shuzo Izumi for his helpful advice and encouragement. The author would like to thank the referees for their helpful suggestions.
Citation
Hirofumi KONDO. "A Nullstellensatz for ideals of $C^\infty$ functions in dimension 2." Hokkaido Math. J. 50 (3) 455 - 462, October 2021. https://doi.org/10.14492/hokmj/2019-201
Information
