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Article: Polynomial Retracts and the Jacobian Conjecture

TitlePolynomial Retracts and the Jacobian Conjecture
Authors
KeywordsMathematics
Issue Date1999
PublisherAmerican Mathematical Society.
Citation
Transactions of the American Mathematical Society, 1999, v. 352 n. 1, p. 477-484 How to Cite?
AbstractLet K[x, y] be the polynomial algebra in two variables over a field K of characteristic 0. A subalgebra R of K[x, y] is called a retract if there is an idempotent homomorphism (a retraction, or projection) phi : K[x, y] --> K[x, y] such that phi(K[x, y]) = R. The presence of other, equivalent, definitions of retracts provides several different methods of studying and applying them, and brings together ideas from combinatorial algebra, homological algebra, and algebraic geometry. In this paper, we characterize all the retracts of K[x, y] up to an automorphism, and give several applications of this characterization, in particular, to the well-known Jacobian conjecture.
Persistent Identifierhttp://hdl.handle.net/10722/48400
ISSN
2015 Impact Factor: 1.196
2015 SCImago Journal Rankings: 2.168

 

DC FieldValueLanguage
dc.contributor.authorShpilrain, Ven_HK
dc.contributor.authorYu, Jen_HK
dc.date.accessioned2008-05-22T04:11:43Z-
dc.date.available2008-05-22T04:11:43Z-
dc.date.issued1999en_HK
dc.identifier.citationTransactions of the American Mathematical Society, 1999, v. 352 n. 1, p. 477-484en_HK
dc.identifier.issn0002-9947en_HK
dc.identifier.urihttp://hdl.handle.net/10722/48400-
dc.description.abstractLet K[x, y] be the polynomial algebra in two variables over a field K of characteristic 0. A subalgebra R of K[x, y] is called a retract if there is an idempotent homomorphism (a retraction, or projection) phi : K[x, y] --> K[x, y] such that phi(K[x, y]) = R. The presence of other, equivalent, definitions of retracts provides several different methods of studying and applying them, and brings together ideas from combinatorial algebra, homological algebra, and algebraic geometry. In this paper, we characterize all the retracts of K[x, y] up to an automorphism, and give several applications of this characterization, in particular, to the well-known Jacobian conjecture.en_HK
dc.format.extent223802 bytes-
dc.format.extent2153 bytes-
dc.format.extent3333 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherAmerican Mathematical Society.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsTransactions of the American Mathematical Society. Copyright © American Mathematical Society.en_HK
dc.rightsFirst published in Transactions of the American Mathematical Society, 1999, v. 352 n. 1, p. 477-484, published by the American Mathematical Society,en_HK
dc.subjectMathematicsen_HK
dc.titlePolynomial Retracts and the Jacobian Conjectureen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0002-9947&volume=352&issue=1&spage=477&epage=484&date=1999&atitle=Polynomial+Retracts+and+the+Jacobian+Conjectureen_HK
dc.identifier.emailShpilrain, V: shpil@submaths.hku.hken_HK
dc.identifier.emailYu, J: yujt@hkusua.hku.hken_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.scopuseid_2-s2.0-22844455374-
dc.identifier.hkuros53249-

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