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Article: On generalized cancellation problem

TitleOn generalized cancellation problem
Authors
Issue Date2004
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 2004, v. 281 n. 1, p. 161-166 How to Cite?
AbstractA well-known cancellation problem of Zariski asks whether for two given domains (fields) K1 and K2, an isomorphism of K1 [t] (K (t)) and K2 [t] (K1 (t)) implies an isomorphism of K1 and K1. In this paper, we address a related problem: whether the ring (field) embedding of K1 [t] (K1 (t)) into K2 [t] (K1 (t)) implies the ring (field) embedding of K1 into K2? Our main result is affirmative: if K1 and K2 are arbitrary domains (fields) of the finite transcendence degree and K1 [t] (K1 (t)) can be embedded into K2 [t] (K2 (t)) then K1 can be embedded into K1. As a consequence, we answer a question of Abhyankar, Eakin and Heinzer [J. Algebra 23 (1972) 310-342]. © 2004 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/75200
ISSN
2015 Impact Factor: 0.66
2015 SCImago Journal Rankings: 1.165
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorBelov, Aen_HK
dc.contributor.authorMakarLimanov, Len_HK
dc.contributor.authorYu, JTen_HK
dc.date.accessioned2010-09-06T07:08:53Z-
dc.date.available2010-09-06T07:08:53Z-
dc.date.issued2004en_HK
dc.identifier.citationJournal Of Algebra, 2004, v. 281 n. 1, p. 161-166en_HK
dc.identifier.issn0021-8693en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75200-
dc.description.abstractA well-known cancellation problem of Zariski asks whether for two given domains (fields) K1 and K2, an isomorphism of K1 [t] (K (t)) and K2 [t] (K1 (t)) implies an isomorphism of K1 and K1. In this paper, we address a related problem: whether the ring (field) embedding of K1 [t] (K1 (t)) into K2 [t] (K1 (t)) implies the ring (field) embedding of K1 into K2? Our main result is affirmative: if K1 and K2 are arbitrary domains (fields) of the finite transcendence degree and K1 [t] (K1 (t)) can be embedded into K2 [t] (K2 (t)) then K1 can be embedded into K1. As a consequence, we answer a question of Abhyankar, Eakin and Heinzer [J. Algebra 23 (1972) 310-342]. © 2004 Elsevier Inc. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_HK
dc.relation.ispartofJournal of Algebraen_HK
dc.titleOn generalized cancellation problemen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0021-8693&volume=281 no1&spage=161&epage=166&date=2004&atitle=On+generalized+cancellation+problemen_HK
dc.identifier.emailYu, JT:yujt@hku.hken_HK
dc.identifier.authorityYu, JT=rp00834en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jalgebra.2004.07.006en_HK
dc.identifier.scopuseid_2-s2.0-4644238310en_HK
dc.identifier.hkuros97906en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-4644238310&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume281en_HK
dc.identifier.issue1en_HK
dc.identifier.spage161en_HK
dc.identifier.epage166en_HK
dc.identifier.isiWOS:000224441800009-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridBelov, A=7202831988en_HK
dc.identifier.scopusauthoridMakarLimanov, L=6603475677en_HK
dc.identifier.scopusauthoridYu, JT=7405530208en_HK

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