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Article: Degree estimate for subalgebras generated by two elements
| Title | Degree estimate for subalgebras generated by two elements |
|---|---|
| Authors | |
| Keywords | Commutators Degree Estimate Free Associative Algebras Jacobians Polynomial Algebras Two-Generated Subalgebras |
| Issue Date | 2008 |
| Citation | Journal Of The European Mathematical Society, 2008, v. 10 n. 2, p. 533-541 How to Cite? |
| Abstract | We 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 Identifier | http://hdl.handle.net/10722/156213 |
| ISSN | 2023 Impact Factor: 2.5 2023 SCImago Journal Rankings: 3.251 |
| References |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | MakarLimanov, L | en_US |
| dc.contributor.author | Yu, JT | en_US |
| dc.date.accessioned | 2012-08-08T08:40:52Z | - |
| dc.date.available | 2012-08-08T08:40:52Z | - |
| dc.date.issued | 2008 | en_US |
| dc.identifier.citation | Journal Of The European Mathematical Society, 2008, v. 10 n. 2, p. 533-541 | en_US |
| dc.identifier.issn | 1435-9855 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10722/156213 | - |
| dc.description.abstract | We 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.language | eng | en_US |
| dc.relation.ispartof | Journal of the European Mathematical Society | en_US |
| dc.subject | Commutators | en_US |
| dc.subject | Degree Estimate | en_US |
| dc.subject | Free Associative Algebras | en_US |
| dc.subject | Jacobians | en_US |
| dc.subject | Polynomial Algebras | en_US |
| dc.subject | Two-Generated Subalgebras | en_US |
| dc.title | Degree estimate for subalgebras generated by two elements | 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 | link_to_subscribed_fulltext | en_US |
| dc.identifier.scopus | eid_2-s2.0-43649102067 | en_US |
| dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-43649102067&selection=ref&src=s&origin=recordpage | en_US |
| dc.identifier.volume | 10 | en_US |
| dc.identifier.issue | 2 | en_US |
| dc.identifier.spage | 533 | en_US |
| dc.identifier.epage | 541 | en_US |
| dc.identifier.scopusauthorid | MakarLimanov, L=6603475677 | en_US |
| dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_US |
| dc.identifier.issnl | 1435-9855 | - |