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Article: On low-dimensional cancellation problems
Title | On low-dimensional cancellation problems |
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Authors | |
Keywords | Birational Cancellation Problems Cancellation Conjecture Of Zariski Good Embeddings Lüroth's Theorem |
Issue Date | 2008 |
Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra |
Citation | Journal Of Algebra, 2008, v. 319 n. 6, p. 2235-2242 How to Cite? |
Abstract | A well-known cancellation problem of Zariski asks when, for two given domains (fields) K1 and K2 over a field k, a k-isomorphism of K1 [t] (K1 (t)) and K2 [t] (K2 (t)) implies a k-isomorphism of K1 and K2. The main results of this article give affirmative answer to the two low-dimensional cases of this problem:. 1. Let K be an affine field over an algebraically closed field k of any characteristic. SupposeK (t) ≃ k (t1, t2, t3), thenK ≃ k (t1, t2) . 2. Let M be a 3-dimensional affine algebraic variety over an algebraically closed field k of any characteristic. LetA = K [x, y, z, w] / M be the coordinate ring of M. SupposeA [t] ≃ k [x1, x2, x3, x4], thenfrac (A) ≃ k (x1, x2, x3), wherefrac (A) is the field of fractions of A. In the case of zero characteristic these results were obtained by Kang in [Ming-chang Kang, A note on the birational cancellation problem, J. Pure Appl. Algebra 77 (1992) 141-154; Ming-chang Kang, The cancellation problem, J. Pure Appl. Algebra 47 (1987) 165-171]. However, the case of finite characteristic is first settled in this article, that answered the questions proposed by Kang in [Ming-chang Kang, A note on the birational cancellation problem, J. Pure Appl. Algebra 77 (1992) 141-154; Ming-chang Kang, The cancellation problem, J. Pure Appl. Algebra 47 (1987) 165-171]. © 2008 Elsevier Inc. All rights reserved. |
Persistent Identifier | http://hdl.handle.net/10722/156205 |
ISSN | 2015 Impact Factor: 0.66 2015 SCImago Journal Rankings: 1.165 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Belov, A | en_US |
dc.contributor.author | Yu, JT | en_US |
dc.date.accessioned | 2012-08-08T08:40:50Z | - |
dc.date.available | 2012-08-08T08:40:50Z | - |
dc.date.issued | 2008 | en_US |
dc.identifier.citation | Journal Of Algebra, 2008, v. 319 n. 6, p. 2235-2242 | en_US |
dc.identifier.issn | 0021-8693 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156205 | - |
dc.description.abstract | A well-known cancellation problem of Zariski asks when, for two given domains (fields) K1 and K2 over a field k, a k-isomorphism of K1 [t] (K1 (t)) and K2 [t] (K2 (t)) implies a k-isomorphism of K1 and K2. The main results of this article give affirmative answer to the two low-dimensional cases of this problem:. 1. Let K be an affine field over an algebraically closed field k of any characteristic. SupposeK (t) ≃ k (t1, t2, t3), thenK ≃ k (t1, t2) . 2. Let M be a 3-dimensional affine algebraic variety over an algebraically closed field k of any characteristic. LetA = K [x, y, z, w] / M be the coordinate ring of M. SupposeA [t] ≃ k [x1, x2, x3, x4], thenfrac (A) ≃ k (x1, x2, x3), wherefrac (A) is the field of fractions of A. In the case of zero characteristic these results were obtained by Kang in [Ming-chang Kang, A note on the birational cancellation problem, J. Pure Appl. Algebra 77 (1992) 141-154; Ming-chang Kang, The cancellation problem, J. Pure Appl. Algebra 47 (1987) 165-171]. However, the case of finite characteristic is first settled in this article, that answered the questions proposed by Kang in [Ming-chang Kang, A note on the birational cancellation problem, J. Pure Appl. Algebra 77 (1992) 141-154; Ming-chang Kang, The cancellation problem, J. Pure Appl. Algebra 47 (1987) 165-171]. © 2008 Elsevier Inc. All rights reserved. | en_US |
dc.language | eng | en_US |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra | en_US |
dc.relation.ispartof | Journal of Algebra | en_US |
dc.rights | Creative Commons: Attribution 3.0 Hong Kong License | - |
dc.subject | Birational Cancellation Problems | en_US |
dc.subject | Cancellation Conjecture Of Zariski | en_US |
dc.subject | Good Embeddings | en_US |
dc.subject | Lüroth's Theorem | en_US |
dc.title | On low-dimensional cancellation problems | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yu, JT:yujt@hku.hk | en_US |
dc.identifier.authority | Yu, JT=rp00834 | en_US |
dc.description.nature | preprint | en_US |
dc.identifier.doi | 10.1016/j.jalgebra.2006.11.036 | en_US |
dc.identifier.scopus | eid_2-s2.0-38849176704 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-38849176704&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 319 | en_US |
dc.identifier.issue | 6 | en_US |
dc.identifier.spage | 2235 | en_US |
dc.identifier.epage | 2242 | en_US |
dc.identifier.isi | WOS:000254349900001 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Belov, A=7202831988 | en_US |
dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_US |