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Article: On the Jacobian Conjecture: Reduction of Coefficients

TitleOn the Jacobian Conjecture: Reduction of Coefficients
Authors
Issue Date1995
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 1995, v. 171 n. 2, p. 515-523 How to Cite?
AbstractWe prove that a polynomial map from R n to itself with non-zero constant Jacobian determinant is a stably tame automorphism if its linear part is the identity and all the coefficients of its higher order terms are non-positive. We also prove that the Jacobian conjecture holds for any number of variables and any field of characteristic zero, if one can show that every polynomial map of R n to itself is injective when it has a non-zero constant Jacobian determinant and has linear part the identity, and all the coefficients of higher order terms are non-negative. The proofs use special properties of matrices with non-positive off-diagonal elements and non-negative principal minors, and of matrices with vanishing principal minors. Furthermore we reduce the Jacobian conjecture to a polynomial matrix problem. Moreover, if the matrix has a positive answer, then every real polynomial automorphism is stably tame. © 1995 Academic Press. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/75345
ISSN
2015 Impact Factor: 0.66
2015 SCImago Journal Rankings: 1.165
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorYu, JTen_HK
dc.date.accessioned2010-09-06T07:10:15Z-
dc.date.available2010-09-06T07:10:15Z-
dc.date.issued1995en_HK
dc.identifier.citationJournal Of Algebra, 1995, v. 171 n. 2, p. 515-523en_HK
dc.identifier.issn0021-8693en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75345-
dc.description.abstractWe prove that a polynomial map from R n to itself with non-zero constant Jacobian determinant is a stably tame automorphism if its linear part is the identity and all the coefficients of its higher order terms are non-positive. We also prove that the Jacobian conjecture holds for any number of variables and any field of characteristic zero, if one can show that every polynomial map of R n to itself is injective when it has a non-zero constant Jacobian determinant and has linear part the identity, and all the coefficients of higher order terms are non-negative. The proofs use special properties of matrices with non-positive off-diagonal elements and non-negative principal minors, and of matrices with vanishing principal minors. Furthermore we reduce the Jacobian conjecture to a polynomial matrix problem. Moreover, if the matrix has a positive answer, then every real polynomial automorphism is stably tame. © 1995 Academic Press. All rights reserved.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.titleOn the Jacobian Conjecture: Reduction of Coefficientsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0021-8693&volume=171&spage=515&epage=523&date=1995&atitle=On+the+Jacobian+Conjecture:+reduction+of+coefficientsen_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.1995.1024en_HK
dc.identifier.scopuseid_2-s2.0-0041574832en_HK
dc.identifier.hkuros20729en_HK
dc.identifier.volume171en_HK
dc.identifier.issue2en_HK
dc.identifier.spage515en_HK
dc.identifier.epage523en_HK
dc.identifier.isiWOS:A1995QF80000011-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridYu, JT=7405530208en_HK

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