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Article: Primitive elements of free metabelian algebras of rank two

TitlePrimitive elements of free metabelian algebras of rank two
Authors
KeywordsAutomorphisms
Free associative algebras
Free metabelian (associative and Lie) algebras
Polynomial algebras
Issue Date2003
PublisherWorld Scientific Publishing Co Pte Ltd. The Journal's web site is located at http://www.worldscinet.com/ijac/ijac.shtml
Citation
International Journal Of Algebra And Computation, 2003, v. 13 n. 1, p. 17-33 How to Cite?
AbstractLet F(x, y) be a relatively free algebra of rank 2 in some variety of algebras over a field K of characteristic 0. In this paper we consider the problem whether p(x, y) ∈ F(x, y) is a primitive element (i.e. an automorphic image of x): (i) If F(x, y)/(p(x, y)) ≅ F(z), the relatively free algebra of rank 1 (ii) If p(f, g) is primitive for some injective endomorphism (f, 9) of F(x, y) (iii) If p(x, y) is primitive in a relatively free algebra of larger rank. These problems have positive solutions for polynomial algebras in two variables. We give the complete answer for the free metabelian associative and Lie algebras and some partial results for free associative algebras.
Persistent Identifierhttp://hdl.handle.net/10722/75477
ISSN
2015 Impact Factor: 0.469
2015 SCImago Journal Rankings: 0.771
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorDrensky, Ven_HK
dc.contributor.authorYu, JTen_HK
dc.date.accessioned2010-09-06T07:11:28Z-
dc.date.available2010-09-06T07:11:28Z-
dc.date.issued2003en_HK
dc.identifier.citationInternational Journal Of Algebra And Computation, 2003, v. 13 n. 1, p. 17-33en_HK
dc.identifier.issn0218-1967en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75477-
dc.description.abstractLet F(x, y) be a relatively free algebra of rank 2 in some variety of algebras over a field K of characteristic 0. In this paper we consider the problem whether p(x, y) ∈ F(x, y) is a primitive element (i.e. an automorphic image of x): (i) If F(x, y)/(p(x, y)) ≅ F(z), the relatively free algebra of rank 1 (ii) If p(f, g) is primitive for some injective endomorphism (f, 9) of F(x, y) (iii) If p(x, y) is primitive in a relatively free algebra of larger rank. These problems have positive solutions for polynomial algebras in two variables. We give the complete answer for the free metabelian associative and Lie algebras and some partial results for free associative algebras.en_HK
dc.languageengen_HK
dc.publisherWorld Scientific Publishing Co Pte Ltd. The Journal's web site is located at http://www.worldscinet.com/ijac/ijac.shtmlen_HK
dc.relation.ispartofInternational Journal of Algebra and Computationen_HK
dc.subjectAutomorphismsen_HK
dc.subjectFree associative algebrasen_HK
dc.subjectFree metabelian (associative and Lie) algebrasen_HK
dc.subjectPolynomial algebrasen_HK
dc.titlePrimitive elements of free metabelian algebras of rank twoen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0218-1967&volume=13&issue=1&spage=17&epage=33&date=2003&atitle=Primitive+elements+of+free+metabelian+algebras+of+rank+twoen_HK
dc.identifier.emailYu, JT:yujt@hku.hken_HK
dc.identifier.authorityYu, JT=rp00834en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1142/S021819670300133Xen_HK
dc.identifier.scopuseid_2-s2.0-0037322086en_HK
dc.identifier.hkuros76903en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0037322086&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume13en_HK
dc.identifier.issue1en_HK
dc.identifier.spage17en_HK
dc.identifier.epage33en_HK
dc.identifier.isiWOS:000182289400002-
dc.publisher.placeSingaporeen_HK
dc.identifier.scopusauthoridDrensky, V=6603826254en_HK
dc.identifier.scopusauthoridYu, JT=7405530208en_HK

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