Commutative Finitely Generated Algebras Satisfying ((yx)x)x = 0 are Solvable

dc.contributor.author Correa, Ivan
dc.contributor.author Hentzel, Irvin
dc.contributor.author Hentzel, Irvin
dc.contributor.department Mathematics
dc.date 2019-12-17T22:20:07.000
dc.date.accessioned 2020-06-30T05:59:46Z
dc.date.available 2020-06-30T05:59:46Z
dc.date.copyright Thu Jan 01 00:00:00 UTC 2009
dc.date.issued 2009-01-01
dc.description.abstract <p>We study commutative, nonassociative algebras satisfying the identity</p> <p>(1) ((<em>yx</em>)<em>x</em>)<em>x</em> = 0</p> <p><em><br /></em>We show that finitely generated algebras over a field <em>K</em> of characteristic ≠ 2 satisfying (1) are solvable. For <em>x</em> in an algebra <em>A</em>, define the multiplicatin operator <em>R<sub>x</sub></em> by <em>yR<sub>x</sub></em> = <em>yx</em>, for all <em>y</em> ∈ <em>A</em>. Our identify is then that <em>R<sub>x</sub></em><sup>3</sup> = 0.</p>
dc.description.comments <p>This article is published as Correa, Ivan, and Irvin Roy Hentzel. "Commutative Finitely Generated Algebras Satisfying ((yx) x) x= 0 are Solvable." <em>Rocky Mountain Journal of Mathematics</em> 39, no. 3 (2009): 757-764. DOI: <a href="http://dx.doi.org/10.1216/RMJ-2009-39-3-757" target="_blank" title="Commutative Finitely Generated Algebras Satisfying ((yx)x)x=0 are Solvable">10.1216/RMJ-2009-39-3-757</a>. Posted with permission.</p>
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dc.identifier archive/lib.dr.iastate.edu/math_pubs/131/
dc.identifier.articleid 1136
dc.identifier.contextkey 10897320
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/131
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/54515
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/131/2009_Hentzel_CommutativeFinitely.pdf|||Fri Jan 14 19:44:30 UTC 2022
dc.source.uri 10.1216/RMJ-2009-39-3-757
dc.subject.disciplines Algebra
dc.subject.disciplines Mathematics
dc.subject.keywords Commutative
dc.subject.keywords solvable
dc.subject.keywords nilpotent
dc.subject.keywords finitely-generated
dc.title Commutative Finitely Generated Algebras Satisfying ((yx)x)x = 0 are Solvable
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication 70506428-9d7c-4c43-bcfa-d89bbb2149e4
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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