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Article: Applications of degree estimate for subalgebras
Title | Applications of degree estimate for subalgebras |
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Authors | |
Keywords | Automorphic Orbits Commutators Coordinate Degree Estimate Free Associative Algebras Jacobians Mal'tsev-Neumann Algebras Retracts Test Elements |
Issue Date | 2011 |
Citation | Comptes Rendus De L'academie Bulgare Des Sciences, 2011, v. 64 n. 2, p. 165-172 How to Cite? |
Abstract | Let 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 Identifier | http://hdl.handle.net/10722/156265 |
ISSN | 2023 Impact Factor: 0.3 2023 SCImago Journal Rankings: 0.160 |
References |
DC Field | Value | Language |
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dc.contributor.author | Li, YC | en_US |
dc.contributor.author | Yu, JT | en_US |
dc.date.accessioned | 2012-08-08T08:41:05Z | - |
dc.date.available | 2012-08-08T08:41:05Z | - |
dc.date.issued | 2011 | en_US |
dc.identifier.citation | Comptes Rendus De L'academie Bulgare Des Sciences, 2011, v. 64 n. 2, p. 165-172 | en_US |
dc.identifier.issn | 1310-1331 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156265 | - |
dc.description.abstract | Let 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.language | eng | en_US |
dc.relation.ispartof | Comptes Rendus de L'Academie Bulgare des Sciences | en_US |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Automorphic Orbits | en_US |
dc.subject | Commutators | en_US |
dc.subject | Coordinate | en_US |
dc.subject | Degree Estimate | en_US |
dc.subject | Free Associative Algebras | en_US |
dc.subject | Jacobians | en_US |
dc.subject | Mal'tsev-Neumann Algebras | en_US |
dc.subject | Retracts | en_US |
dc.subject | Test Elements | en_US |
dc.title | Applications of degree estimate for subalgebras | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yu, JT:yujt@hku.hk | en_US |
dc.identifier.authority | Yu, JT=rp00834 | en_US |
dc.description.nature | preprint | - |
dc.identifier.scopus | eid_2-s2.0-79952358004 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-79952358004&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 64 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.spage | 165 | en_US |
dc.identifier.epage | 172 | en_US |
dc.publisher.place | Bulgaria | en_US |
dc.identifier.scopusauthorid | Li, YC=37011043100 | en_US |
dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_US |
dc.identifier.issnl | 1310-1331 | - |