RT Journal Article
T1 On the nullstellensätze for stein spaces and C-analytic sets.
A1 Acquistapace, Francesca
A1 Broglia, Fabrizio
A1 Fernando Galván, José Francisco
AB In this work we prove the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X ⊂ Rn in terms of the saturation of Łojasiewicz’s radical in O(X): The ideal I(Ƶ(a)) of the zero-set Ƶ(a) of an ideal a of O(X) coincides with the saturation (Formula presented) of Łojasiewicz’s radical (Formula presented). If Ƶ(a) has ‘good properties’ concerning Hilbert’s 17th Problem, then I(Ƶ(a)) = (Formula presented) where (Formula presented) stands for the real radical of a. The same holds if we replace (Formula presented) with the real-analytic radical (Formula presented) of a, which is a natural generalization of the real radical ideal in the C-analytic setting. We revisit the classical results concerning (Hilbert’s) Nullstellensatz in the framework of (complex) Stein spaces. Let a be a saturated ideal of O(Rn) and YRn the germ of the support of the coherent sheaf that extends aORn to a suitable complex open neighborhood of Rn. We study the relationship between a normal primary decomposition of a and the decomposition of YRn as the union of its irreducible components. If a:= p is prime, then I(Ƶ(p)) = p if and only if the (complex) dimension of YRn coincides with the (real) dimension of Ƶ(p).
PB American Mathematical Society
SN 0002-9947
YR 2016
FD 2016
LK https://hdl.handle.net/20.500.14352/24540
UL https://hdl.handle.net/20.500.14352/24540
LA eng
NO Spanish GAAR
NO Italian GNSAGA of INdAM and MIUR
NO Department of Algebra at the Universidad Complutense de Madrid
NO Department of Mathematics at the Universit`a di Pisa.
DS Docta Complutense
RD 9 abr 2025