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Article: Equivalence of polynomials under automorphisms of K [x, y]

TitleEquivalence of polynomials under automorphisms of K [x, y]
Authors
Issue Date2007
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/jpaa
Citation
Journal Of Pure And Applied Algebra, 2007, v. 209 n. 1, p. 71-78 How to Cite?
AbstractLet K [x, y] be the algebra of polynomials in two variables over an arbitrary field K. We show that if the maximum of the x- and y-degrees of a given polynomial p (x, y) cannot be decreased by a single triangular or linear automorphism of K [x, y], then it cannot be decreased by any automorphism of K [x, y]. If K is an algebraically closed constructible field, this result yields an algorithm for deciding whether or not two polynomials p, q ∈ K [x, y] are equivalent under an automorphism of K [x, y]. We also show that if there is an automorphism of K [x, y] taking p to q, then it is "almost" unique. More precisely: if an automorphism α of K [x, y] is not conjugate to a triangular or linear automorphism, then any polynomial invariant (or even semiinvariant) under α is a constant. © 2006 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156172
ISSN
2015 Impact Factor: 0.669
2015 SCImago Journal Rankings: 0.990
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorMakarLimanov, Len_US
dc.contributor.authorShpilrain, Ven_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:42Z-
dc.date.available2012-08-08T08:40:42Z-
dc.date.issued2007en_US
dc.identifier.citationJournal Of Pure And Applied Algebra, 2007, v. 209 n. 1, p. 71-78en_US
dc.identifier.issn0022-4049en_US
dc.identifier.urihttp://hdl.handle.net/10722/156172-
dc.description.abstractLet K [x, y] be the algebra of polynomials in two variables over an arbitrary field K. We show that if the maximum of the x- and y-degrees of a given polynomial p (x, y) cannot be decreased by a single triangular or linear automorphism of K [x, y], then it cannot be decreased by any automorphism of K [x, y]. If K is an algebraically closed constructible field, this result yields an algorithm for deciding whether or not two polynomials p, q ∈ K [x, y] are equivalent under an automorphism of K [x, y]. We also show that if there is an automorphism of K [x, y] taking p to q, then it is "almost" unique. More precisely: if an automorphism α of K [x, y] is not conjugate to a triangular or linear automorphism, then any polynomial invariant (or even semiinvariant) under α is a constant. © 2006 Elsevier Ltd. All rights reserved.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/jpaaen_US
dc.relation.ispartofJournal of Pure and Applied Algebraen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleEquivalence of polynomials under automorphisms of K [x, y]en_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturepreprinten_US
dc.identifier.doi10.1016/j.jpaa.2006.05.005en_US
dc.identifier.scopuseid_2-s2.0-33751525145en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33751525145&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume209en_US
dc.identifier.issue1en_US
dc.identifier.spage71en_US
dc.identifier.epage78en_US
dc.identifier.isiWOS:000243862300004-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridMakarLimanov, L=6603475677en_US
dc.identifier.scopusauthoridShpilrain, V=6603904879en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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