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Article: On low-dimensional cancellation problems

TitleOn low-dimensional cancellation problems
Authors
KeywordsBirational Cancellation Problems
Cancellation Conjecture Of Zariski
Good Embeddings
Lüroth's Theorem
Issue Date2008
PublisherAcademic 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?
AbstractA 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 Identifierhttp://hdl.handle.net/10722/156205
ISSN
2015 Impact Factor: 0.66
2015 SCImago Journal Rankings: 1.165
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorBelov, Aen_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:50Z-
dc.date.available2012-08-08T08:40:50Z-
dc.date.issued2008en_US
dc.identifier.citationJournal Of Algebra, 2008, v. 319 n. 6, p. 2235-2242en_US
dc.identifier.issn0021-8693en_US
dc.identifier.urihttp://hdl.handle.net/10722/156205-
dc.description.abstractA 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.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_US
dc.relation.ispartofJournal of Algebraen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBirational Cancellation Problemsen_US
dc.subjectCancellation Conjecture Of Zariskien_US
dc.subjectGood Embeddingsen_US
dc.subjectLüroth's Theoremen_US
dc.titleOn low-dimensional cancellation problemsen_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.jalgebra.2006.11.036en_US
dc.identifier.scopuseid_2-s2.0-38849176704en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-38849176704&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume319en_US
dc.identifier.issue6en_US
dc.identifier.spage2235en_US
dc.identifier.epage2242en_US
dc.identifier.isiWOS:000254349900001-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridBelov, A=7202831988en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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