A note on proper polynomial maps

dc.contributor.author	Sakkalis, T	en
dc.date.accessioned	2014-06-06T06:46:25Z
dc.date.available	2014-06-06T06:46:25Z
dc.date.issued	2005	en
dc.identifier.issn	00927872	en
dc.identifier.uri	http://dx.doi.org/10.1081/AGB-200058543	en
dc.identifier.uri	http://62.217.125.90/xmlui/handle/123456789/2992
dc.subject	Jacobian conjecture	en
dc.subject	Proper polynomial maps	en
dc.subject	Strictly convex maps	en
dc.title	A note on proper polynomial maps	en
heal.type	journalArticle	en
heal.identifier.primary	10.1081/AGB-200058543	en
heal.publicationDate	2005	en
heal.abstract	In this note it is proved that certain level sets of some real proper polynomial maps are nothing but spheres. As an application of this, we provide new proofs of Theorems 1.1, 1.2 and of the fundamental theorem of algebra. In addition, we show that every strictly convex (concave) polynomial map is proper. The latter implies that every real polynomial map g(x): Rn → Rn, whose Jacobian matrix is symmetric and has nonzero eigenvalues of the same sign, is a homeomorphism of Rn onto Rn.	en
heal.journalName	Communications in Algebra	en
dc.identifier.issue	9	en
dc.identifier.volume	33	en
dc.identifier.doi	10.1081/AGB-200058543	en
dc.identifier.spage	3359	en
dc.identifier.epage	3365	en