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Article: Polynomial Retracts and the Jacobian Conjecture
Title  Polynomial Retracts and the Jacobian Conjecture 

Authors  
Keywords  Mathematics 
Issue Date  1999 
Publisher  American Mathematical Society. 
Citation  Transactions of the American Mathematical Society, 1999, v. 352 n. 1, p. 477484 How to Cite? 
Abstract  Let 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 wellknown Jacobian conjecture. 
Persistent Identifier  http://hdl.handle.net/10722/48400 
ISSN  2015 Impact Factor: 1.196 2015 SCImago Journal Rankings: 2.168 
DC Field  Value  Language 

dc.contributor.author  Shpilrain, V  en_HK 
dc.contributor.author  Yu, J  en_HK 
dc.date.accessioned  20080522T04:11:43Z   
dc.date.available  20080522T04:11:43Z   
dc.date.issued  1999  en_HK 
dc.identifier.citation  Transactions of the American Mathematical Society, 1999, v. 352 n. 1, p. 477484  en_HK 
dc.identifier.issn  00029947  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/48400   
dc.description.abstract  Let 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 wellknown Jacobian conjecture.  en_HK 
dc.format.extent  223802 bytes   
dc.format.extent  2153 bytes   
dc.format.extent  3333 bytes   
dc.format.mimetype  application/pdf   
dc.format.mimetype  text/plain   
dc.format.mimetype  text/plain   
dc.language  eng  en_HK 
dc.publisher  American Mathematical Society.  en_HK 
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.rights  Transactions of the American Mathematical Society. Copyright © American Mathematical Society.  en_HK 
dc.rights  First published in Transactions of the American Mathematical Society, 1999, v. 352 n. 1, p. 477484, published by the American Mathematical Society,  en_HK 
dc.subject  Mathematics  en_HK 
dc.title  Polynomial Retracts and the Jacobian Conjecture  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=00029947&volume=352&issue=1&spage=477&epage=484&date=1999&atitle=Polynomial+Retracts+and+the+Jacobian+Conjecture  en_HK 
dc.identifier.email  Shpilrain, V: shpil@submaths.hku.hk  en_HK 
dc.identifier.email  Yu, J: yujt@hkusua.hku.hk  en_HK 
dc.description.nature  published_or_final_version  en_HK 
dc.identifier.scopus  eid_2s2.022844455374   
dc.identifier.hkuros  53249   