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Article: Polynomial Retracts and the Jacobian Conjecture
Title | Polynomial Retracts and the Jacobian Conjecture |
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Authors | |
Keywords | Mathematics |
Issue Date | 1999 |
Publisher | American Mathematical Society. |
Citation | Transactions of the American Mathematical Society, 1999, v. 352 n. 1, p. 477-484 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 well-known Jacobian conjecture. |
Persistent Identifier | http://hdl.handle.net/10722/48400 |
ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 1.581 |
DC Field | Value | Language |
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dc.contributor.author | Shpilrain, V | en_HK |
dc.contributor.author | Yu, J | en_HK |
dc.date.accessioned | 2008-05-22T04:11:43Z | - |
dc.date.available | 2008-05-22T04:11:43Z | - |
dc.date.issued | 1999 | en_HK |
dc.identifier.citation | Transactions of the American Mathematical Society, 1999, v. 352 n. 1, p. 477-484 | en_HK |
dc.identifier.issn | 0002-9947 | 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 well-known 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 | 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. 477-484, 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=0002-9947&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_2-s2.0-22844455374 | - |
dc.identifier.hkuros | 53249 | - |
dc.identifier.issnl | 0002-9947 | - |