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Article: Remarks on the Jacobian Conjecture

TitleRemarks on the Jacobian Conjecture
Authors
Issue Date1997
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 1997, v. 188 n. 1, p. 90-96 How to Cite?
AbstractLetF(F1,...,Fn)∈(C[X1,...,X n])nwith det(J(F))∈C* and letMi(Xi,Y)=mi0(Y)+mi1(Y)X i+···+midi(Y)X i d i∈C[Xi,Y]C[X i,Y1,...,Yn] be the minimal polynomial ofFoverC(Xi). We prove thatmi0(Y),...,midi(Y) have no common zeros inCn. As a direct consequence, we obtain flatness ofC[F,Xi] overC[F] for everyi. As applications, we obtain simple algebraic proofs of the following two known results: (i) A birational polynomial map fromCnintoCnwith det(J(F))∈C* is actually an automorphism; (ii) an injective polynomial map fromCnintoCnis also an automorphism. © 1997 Academic Press.
Persistent Identifierhttp://hdl.handle.net/10722/75225
ISSN
2015 Impact Factor: 0.66
2015 SCImago Journal Rankings: 1.165
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorYu, JTen_HK
dc.date.accessioned2010-09-06T07:09:07Z-
dc.date.available2010-09-06T07:09:07Z-
dc.date.issued1997en_HK
dc.identifier.citationJournal Of Algebra, 1997, v. 188 n. 1, p. 90-96en_HK
dc.identifier.issn0021-8693en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75225-
dc.description.abstractLetF(F1,...,Fn)∈(C[X1,...,X n])nwith det(J(F))∈C* and letMi(Xi,Y)=mi0(Y)+mi1(Y)X i+···+midi(Y)X i d i∈C[Xi,Y]C[X i,Y1,...,Yn] be the minimal polynomial ofFoverC(Xi). We prove thatmi0(Y),...,midi(Y) have no common zeros inCn. As a direct consequence, we obtain flatness ofC[F,Xi] overC[F] for everyi. As applications, we obtain simple algebraic proofs of the following two known results: (i) A birational polynomial map fromCnintoCnwith det(J(F))∈C* is actually an automorphism; (ii) an injective polynomial map fromCnintoCnis also an automorphism. © 1997 Academic Press.en_HK
dc.languageengen_HK
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_HK
dc.relation.ispartofJournal of Algebraen_HK
dc.titleRemarks on the Jacobian Conjectureen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0021-8693&volume=188&spage=90&epage=96&date=1997&atitle=Remarks+on+the+Jacobian+conjectureen_HK
dc.identifier.emailYu, JT:yujt@hku.hken_HK
dc.identifier.authorityYu, JT=rp00834en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1006/jabr.1996.6816en_HK
dc.identifier.scopuseid_2-s2.0-0040056382en_HK
dc.identifier.hkuros36718en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0040056382&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume188en_HK
dc.identifier.issue1en_HK
dc.identifier.spage90en_HK
dc.identifier.epage96en_HK
dc.identifier.isiWOS:A1997WJ54700005-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridYu, JT=7405530208en_HK

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