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Article: On the Jacobian Conjecture: Reduction of Coefficients
Title | On the Jacobian Conjecture: Reduction of Coefficients |
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Authors | |
Issue Date | 1995 |
Publisher | Academic 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? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/75345 |
ISSN | 2015 Impact Factor: 0.66 2015 SCImago Journal Rankings: 1.165 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Yu, JT | en_HK |
dc.date.accessioned | 2010-09-06T07:10:15Z | - |
dc.date.available | 2010-09-06T07:10:15Z | - |
dc.date.issued | 1995 | en_HK |
dc.identifier.citation | Journal Of Algebra, 1995, v. 171 n. 2, p. 515-523 | en_HK |
dc.identifier.issn | 0021-8693 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/75345 | - |
dc.description.abstract | We 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.language | eng | en_HK |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra | en_HK |
dc.relation.ispartof | Journal of Algebra | en_HK |
dc.title | On the Jacobian Conjecture: Reduction of Coefficients | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+coefficients | en_HK |
dc.identifier.email | Yu, JT:yujt@hku.hk | en_HK |
dc.identifier.authority | Yu, JT=rp00834 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1006/jabr.1995.1024 | en_HK |
dc.identifier.scopus | eid_2-s2.0-0041574832 | en_HK |
dc.identifier.hkuros | 20729 | en_HK |
dc.identifier.volume | 171 | en_HK |
dc.identifier.issue | 2 | en_HK |
dc.identifier.spage | 515 | en_HK |
dc.identifier.epage | 523 | en_HK |
dc.identifier.isi | WOS:A1995QF80000011 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_HK |