RT Journal Article
T1 On The Irreducible Components Of A Semialgebraic Set
A1 Gamboa Mutuberria, José Manuel
A1 Fernando Galván, José Francisco
AB In this work we define a semialgebraic set S Rn to be irreducible if the noetherian ring of Nash functions on S is an integral domain. Keeping this notion we develop a satisfactory theory of irreducible components of semialgebraic sets, and we use it fruitfully to approach four classical problems in Real Geometry for the ring : Substitution Theorem, Positivstellens¨atze, 17th Hilbert Problem and real Nullstellensatz, whose solution was known just in case S = M is an affine Nash manifold. In fact, wegive full characterizations of the families of semialgebraic sets for which these classical results are true.
PB World Scientific Publ
SN 0129-167X
YR 2012
FD 2012
LK https://hdl.handle.net/20.500.14352/42179
UL https://hdl.handle.net/20.500.14352/42179
NO Spanish GEOR[MTM2011-22435]; GAAR Grupos[UCM 910444]
DS Docta Complutense
RD 4 abr 2025