File Download
  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Applications of degree estimate for subalgebras

TitleApplications of degree estimate for subalgebras
Authors
KeywordsAutomorphic Orbits
Commutators
Coordinate
Degree Estimate
Free Associative Algebras
Jacobians
Mal'tsev-Neumann Algebras
Retracts
Test Elements
Issue Date2011
Citation
Comptes Rendus De L'academie Bulgare Des Sciences, 2011, v. 64 n. 2, p. 165-172 How to Cite?
AbstractLet K be a field of positive characteristic and K (x,y) be the free algebra of rank two over K. Based on the degree estimate done by Y.-C. Li and J.-T. Yu, we extend the results of S. J. Gong and J. T. Yu's results: (1) An element p(x,y) ∈ K 〈x,y〉 is a test element if and only if p(x,y) does not belong to any proper retract of K 〈x,y〉 (2) Every endomorphism preserving the automorphic orbit of a nonconstant element of K 〈x,y〉 is an automorphism; (3) If there exists some injective endomorphism φ of K 〈x,y〉 such that φ (p(x,y)) = x where p(x,y) ∈ K〈x,y〉, then p(x; y) is a coordinate. And we reprove that all the automorphisms of K〈x,y〉 are tame. Moreover, we also give counterexamples for two conjectures established by Leonid Makar-Limanov, V. Drensky and J.-T. Yu in the positive characteristic case.
Persistent Identifierhttp://hdl.handle.net/10722/156265
ISSN
2015 Impact Factor: 0.233
References

 

DC FieldValueLanguage
dc.contributor.authorLi, YCen_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:41:05Z-
dc.date.available2012-08-08T08:41:05Z-
dc.date.issued2011en_US
dc.identifier.citationComptes Rendus De L'academie Bulgare Des Sciences, 2011, v. 64 n. 2, p. 165-172en_US
dc.identifier.issn1310-1331en_US
dc.identifier.urihttp://hdl.handle.net/10722/156265-
dc.description.abstractLet K be a field of positive characteristic and K (x,y) be the free algebra of rank two over K. Based on the degree estimate done by Y.-C. Li and J.-T. Yu, we extend the results of S. J. Gong and J. T. Yu's results: (1) An element p(x,y) ∈ K 〈x,y〉 is a test element if and only if p(x,y) does not belong to any proper retract of K 〈x,y〉 (2) Every endomorphism preserving the automorphic orbit of a nonconstant element of K 〈x,y〉 is an automorphism; (3) If there exists some injective endomorphism φ of K 〈x,y〉 such that φ (p(x,y)) = x where p(x,y) ∈ K〈x,y〉, then p(x; y) is a coordinate. And we reprove that all the automorphisms of K〈x,y〉 are tame. Moreover, we also give counterexamples for two conjectures established by Leonid Makar-Limanov, V. Drensky and J.-T. Yu in the positive characteristic case.en_US
dc.languageengen_US
dc.relation.ispartofComptes Rendus de L'Academie Bulgare des Sciencesen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectAutomorphic Orbitsen_US
dc.subjectCommutatorsen_US
dc.subjectCoordinateen_US
dc.subjectDegree Estimateen_US
dc.subjectFree Associative Algebrasen_US
dc.subjectJacobiansen_US
dc.subjectMal'tsev-Neumann Algebrasen_US
dc.subjectRetractsen_US
dc.subjectTest Elementsen_US
dc.titleApplications of degree estimate for subalgebrasen_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturepreprint-
dc.identifier.scopuseid_2-s2.0-79952358004en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79952358004&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume64en_US
dc.identifier.issue2en_US
dc.identifier.spage165en_US
dc.identifier.epage172en_US
dc.publisher.placeBulgariaen_US
dc.identifier.scopusauthoridLi, YC=37011043100en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats