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Article: Degree estimate for subalgebras generated by two elements

TitleDegree estimate for subalgebras generated by two elements
Authors
KeywordsCommutators
Degree Estimate
Free Associative Algebras
Jacobians
Polynomial Algebras
Two-Generated Subalgebras
Issue Date2008
Citation
Journal Of The European Mathematical Society, 2008, v. 10 n. 2, p. 533-541 How to Cite?
AbstractWe develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture. © European Mathematical Society 2008.
Persistent Identifierhttp://hdl.handle.net/10722/156213
ISSN
2015 Impact Factor: 1.95
2015 SCImago Journal Rankings: 3.658
References

 

DC FieldValueLanguage
dc.contributor.authorMakarLimanov, Len_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:52Z-
dc.date.available2012-08-08T08:40:52Z-
dc.date.issued2008en_US
dc.identifier.citationJournal Of The European Mathematical Society, 2008, v. 10 n. 2, p. 533-541en_US
dc.identifier.issn1435-9855en_US
dc.identifier.urihttp://hdl.handle.net/10722/156213-
dc.description.abstractWe develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture. © European Mathematical Society 2008.en_US
dc.languageengen_US
dc.relation.ispartofJournal of the European Mathematical Societyen_US
dc.subjectCommutatorsen_US
dc.subjectDegree Estimateen_US
dc.subjectFree Associative Algebrasen_US
dc.subjectJacobiansen_US
dc.subjectPolynomial Algebrasen_US
dc.subjectTwo-Generated Subalgebrasen_US
dc.titleDegree estimate for subalgebras generated by two elementsen_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.scopuseid_2-s2.0-43649102067en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-43649102067&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume10en_US
dc.identifier.issue2en_US
dc.identifier.spage533en_US
dc.identifier.epage541en_US
dc.identifier.scopusauthoridMakarLimanov, L=6603475677en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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