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Article: Gröbner bases and the Nagata automorphism

TitleGröbner bases and the Nagata automorphism
Authors
Issue Date1999
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/jpaa
Citation
Journal Of Pure And Applied Algebra, 1999, v. 135 n. 2, p. 135-153 How to Cite?
AbstractWe study different properties of the Nagata automorphism of the polynomial algebra in three variables and extend them to other automorphisms of polynomial algebras and algebras close to them. In particular, we propose two approaches to the Nagata conjecture: via the theory of Gröbner bases and trying to lift the Nagata automorphism to an automorphism of the free associative algebra. We show that the reduced Gröbner basis of three face polynomials of the Nagata automorphism obtained by substituting a variable by zero does not produce an automorphism, independently of the "tag" monomial ordering, contrary to the two variable case. We construct examples related to Nagata's automorphism which show different aspects of this problem. We formulate a conjecture which implies Nagata's conjecture. We also construct an explicit lifting of the Nagata automorphism to the free metabelian associative algebra. Finally, we show that the method to determine whether an endomorphism of K[X] is an automorphism is based on a general fact for the ideals of arbitrary free algebras and works also for other algebraic systems such as groups and semigroups, etc. © 1999 Elsevier Science B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156078
ISSN
2015 Impact Factor: 0.669
2015 SCImago Journal Rankings: 0.990
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorDrensky, Ven_US
dc.contributor.authorGutierrez, Jen_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:18Z-
dc.date.available2012-08-08T08:40:18Z-
dc.date.issued1999en_US
dc.identifier.citationJournal Of Pure And Applied Algebra, 1999, v. 135 n. 2, p. 135-153en_US
dc.identifier.issn0022-4049en_US
dc.identifier.urihttp://hdl.handle.net/10722/156078-
dc.description.abstractWe study different properties of the Nagata automorphism of the polynomial algebra in three variables and extend them to other automorphisms of polynomial algebras and algebras close to them. In particular, we propose two approaches to the Nagata conjecture: via the theory of Gröbner bases and trying to lift the Nagata automorphism to an automorphism of the free associative algebra. We show that the reduced Gröbner basis of three face polynomials of the Nagata automorphism obtained by substituting a variable by zero does not produce an automorphism, independently of the "tag" monomial ordering, contrary to the two variable case. We construct examples related to Nagata's automorphism which show different aspects of this problem. We formulate a conjecture which implies Nagata's conjecture. We also construct an explicit lifting of the Nagata automorphism to the free metabelian associative algebra. Finally, we show that the method to determine whether an endomorphism of K[X] is an automorphism is based on a general fact for the ideals of arbitrary free algebras and works also for other algebraic systems such as groups and semigroups, etc. © 1999 Elsevier Science B.V. All rights reserved.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/jpaaen_US
dc.relation.ispartofJournal of Pure and Applied Algebraen_US
dc.titleGröbner bases and the Nagata automorphismen_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.doi10.1016/S0022-4049(97)00146-1-
dc.identifier.scopuseid_2-s2.0-0033556958en_US
dc.identifier.hkuros46970-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0033556958&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume135en_US
dc.identifier.issue2en_US
dc.identifier.spage135en_US
dc.identifier.epage153en_US
dc.identifier.isiWOS:000078511100003-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridDrensky, V=6603826254en_US
dc.identifier.scopusauthoridGutierrez, J=7401652951en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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