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Article: Primitive, almost primitive, test, and Δ-primitive elements of free algebras with the Nielsen-Schreier property

TitlePrimitive, almost primitive, test, and Δ-primitive elements of free algebras with the Nielsen-Schreier property
Authors
Issue Date2000
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 2000, v. 228 n. 2, p. 603-623 How to Cite?
AbstractWe study generalized primitive elements of free algebras of finite ranks with the Nielsen-Schreier property and their automorphic orbits. A primitive element of a free algebra is an element of some free generating set of this algebra. Almost primitive elements are not primitive elements which are primitive in any proper subalgebra. Δ-primitive elements are elements whose partial derivatives generate the same one-sided ideal of the universal multiplicative envelope algebra of a free algebra as the set of free generators generate. We prove that an endomorphism preserving an automorphic orbit of a nonzero element of a free algebra of rank two is an automorphism. An algorithm to determine test elements of free algebras of rank two is described. A series of almost primitive elements is constructed and new examples of test elements are given. We prove that if the rank n of the free Lie algebra L is even, n=2m, then any Δ-primitive element of L is an automorphic image of the element w=[x1,x2]+···+[x2m-1,x2m], there are no Δ-primitive elements of L if n is odd, and the group of automorphisms of the algebra L acts transitively on the set of all Δ-primitive elements. © 2000 Academic Press.
Persistent Identifierhttp://hdl.handle.net/10722/156084
ISSN
2015 Impact Factor: 0.66
2015 SCImago Journal Rankings: 1.165
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorMikhalev, AAen_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:20Z-
dc.date.available2012-08-08T08:40:20Z-
dc.date.issued2000en_US
dc.identifier.citationJournal Of Algebra, 2000, v. 228 n. 2, p. 603-623en_US
dc.identifier.issn0021-8693en_US
dc.identifier.urihttp://hdl.handle.net/10722/156084-
dc.description.abstractWe study generalized primitive elements of free algebras of finite ranks with the Nielsen-Schreier property and their automorphic orbits. A primitive element of a free algebra is an element of some free generating set of this algebra. Almost primitive elements are not primitive elements which are primitive in any proper subalgebra. Δ-primitive elements are elements whose partial derivatives generate the same one-sided ideal of the universal multiplicative envelope algebra of a free algebra as the set of free generators generate. We prove that an endomorphism preserving an automorphic orbit of a nonzero element of a free algebra of rank two is an automorphism. An algorithm to determine test elements of free algebras of rank two is described. A series of almost primitive elements is constructed and new examples of test elements are given. We prove that if the rank n of the free Lie algebra L is even, n=2m, then any Δ-primitive element of L is an automorphic image of the element w=[x1,x2]+···+[x2m-1,x2m], there are no Δ-primitive elements of L if n is odd, and the group of automorphisms of the algebra L acts transitively on the set of all Δ-primitive elements. © 2000 Academic Press.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_US
dc.relation.ispartofJournal of Algebraen_US
dc.titlePrimitive, almost primitive, test, and Δ-primitive elements of free algebras with the Nielsen-Schreier propertyen_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.doi10.1006/jabr.2000.8288en_US
dc.identifier.scopuseid_2-s2.0-0034658810en_US
dc.identifier.hkuros53209-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0034658810&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume228en_US
dc.identifier.issue2en_US
dc.identifier.spage603en_US
dc.identifier.epage623en_US
dc.identifier.isiWOS:000087678800014-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridMikhalev, AA=7007020926en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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