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A global Nullstellensatz for ideals of Denjoy-Carleman functions


Authors: Francesca Acquistapace, Fabrizio Broglia and Andreea C. Nicoara
Journal: Proc. Amer. Math. Soc. 144 (2016), 2067-2071
MSC (2010): Primary 26E10, 46E25; Secondary 11E25
DOI: https://doi.org/10.1090/proc/12847
Published electronically: September 15, 2015
MathSciNet review: 3460167
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Abstract: We prove a Nullstellensatz result for global ideals of Denjoy-
Carleman quasi-analytic functions in both finitely generated and infinitely generated cases.


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Additional Information

Francesca Acquistapace
Affiliation: Dipartimento di Matematica, Università degli Studi di Pisa, Largo Bruno Ponte- corvo, 5, 56127 Pisa, Italy
Email: acquistf@dm.unipi.it

Fabrizio Broglia
Affiliation: Dipartimento di Matematica, Università degli Studi di Pisa, Largo Bruno Ponte- corvo, 5, 56127 Pisa, Italy
Email: broglia@dm.unipi.it

Andreea C. Nicoara
Affiliation: School of Mathematics, Trinity College, Dublin, College Green, Dublin 2, Ireland
Email: anicoara@maths.tcd.ie

DOI: https://doi.org/10.1090/proc/12847
Keywords: Denjoy-Carleman quasianalytic classes, ideals of Denjoy-Carleman functions, Nullstellensatz, closed ideal, real Nullstellensatz, radical ideal, {\L}ojasiewicz radical ideal, saturation of an ideal
Received by editor(s): December 31, 2014
Received by editor(s) in revised form: April 25, 2015, and May 28, 2015
Published electronically: September 15, 2015
Additional Notes: The work presented in this paper was initiated while the authors were visiting the American Institute of Mathematics, Palo Alto, CA, for a SQuaRE workshop. The authors are grateful to AIM for the hospitality and financial support.
Communicated by: Lev Borisov
Article copyright: © Copyright 2015 American Mathematical Society

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