A Nullstellensatz for Lojasiewicz ideals

作者：Acquistapace Francesca^*; Broglia Fabrizio; Nicoara Andreea

来源：Revista Matematica Iberoamericana, 2014, 30(4): 1479-1487.

DOI：10.4171/RMI/822

• Nullstellensatz
• closed ideal
• real Nullstellensatz
• radical ideal
• Lojasiewicz radical ideal
• real ideal
• real analytic ideal
• Whitney closure
• saturation of an ideal

For an ideal of smooth functions a that is either Lojasiewicz or weakly Lojasiewicz, we give a complete characterization of the ideal of functions vanishing on its variety I(Z(a)) in terms of the global Lojasiewicz radical and Whitney closure. We also prove that the Lojasiewicz radical of such an ideal is analytic-like in the sense that its saturation equals its Whitney closure. This allows us to revisit Nullstellensatz results due to Bochnak and Adkins-Leahy and to resolve positively a modification of the Nullstellensatz conjecture due to Bochnak.

• 出版日期2014