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Article: Cancellation problems and dimension theory

TitleCancellation problems and dimension theory
Authors
Issue Date2006
PublisherTaylor & Francis Inc. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00927872.asp
Citation
Communications In Algebra, 2006, v. 34 n. 4, p. 1521-1540 How to Cite?
AbstractA well-known cancellation problem of Zariski asks - for two given domains (fields, respectively) K 1 and K 2 over a field k - whether the k -isomorphism of K1[t] (K(t), respectively) and K2[t] (K2(t), respectively) implies the k -isomorphism of K1 and K2. In this article, we address and systematically study a related problem: whether the k-embedding from K1[t](K1(t), respectively) into K2[t](K2(t), respectively) implies the k-embedding from K 1 into K2. Our results are affirmative: if K1 and K 2 are affine domains over an arbitrary field k, and K1[t] can be k -embedded into K2 [t], then K 1 can be k -embedded into K2; if K1 and K2 are affine fields over an arbitrary field k, and K1 t) can be k-embedded into K2 (t), then K1 can be k-embedded into K2. Similar results are obtained for some general nonaffine domains and nonaffine fields. These results were obtained in Belov et al. (preprint) together with L. Makar-Limanov. In this article we give an alternative proof, show connection with dimension theory, consider the case of infinite transcendental degree, and present some applications and surroundings.
Persistent Identifierhttp://hdl.handle.net/10722/156161
ISSN
2015 Impact Factor: 0.368
2015 SCImago Journal Rankings: 0.649
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorBelov, Aen_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:39Z-
dc.date.available2012-08-08T08:40:39Z-
dc.date.issued2006en_US
dc.identifier.citationCommunications In Algebra, 2006, v. 34 n. 4, p. 1521-1540en_US
dc.identifier.issn0092-7872en_US
dc.identifier.urihttp://hdl.handle.net/10722/156161-
dc.description.abstractA well-known cancellation problem of Zariski asks - for two given domains (fields, respectively) K 1 and K 2 over a field k - whether the k -isomorphism of K1[t] (K(t), respectively) and K2[t] (K2(t), respectively) implies the k -isomorphism of K1 and K2. In this article, we address and systematically study a related problem: whether the k-embedding from K1[t](K1(t), respectively) into K2[t](K2(t), respectively) implies the k-embedding from K 1 into K2. Our results are affirmative: if K1 and K 2 are affine domains over an arbitrary field k, and K1[t] can be k -embedded into K2 [t], then K 1 can be k -embedded into K2; if K1 and K2 are affine fields over an arbitrary field k, and K1 t) can be k-embedded into K2 (t), then K1 can be k-embedded into K2. Similar results are obtained for some general nonaffine domains and nonaffine fields. These results were obtained in Belov et al. (preprint) together with L. Makar-Limanov. In this article we give an alternative proof, show connection with dimension theory, consider the case of infinite transcendental degree, and present some applications and surroundings.en_US
dc.languageengen_US
dc.publisherTaylor & Francis Inc. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00927872.aspen_US
dc.relation.ispartofCommunications in Algebraen_US
dc.titleCancellation problems and dimension theoryen_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1080/00927870500455064en_US
dc.identifier.scopuseid_2-s2.0-33645762239en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33645762239&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume34en_US
dc.identifier.issue4en_US
dc.identifier.spage1521en_US
dc.identifier.epage1540en_US
dc.identifier.isiWOS:000237381500020-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridBelov, A=7202831988en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US
dc.identifier.citeulike642866-

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