Generalized Derivations with Power Central Values on Multilinear Polynomials on Right Ideals

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dc.contributor.authorArgac, N.
dc.contributor.authorDe Filippis, V.
dc.contributor.authorInceboz, H. G.
dc.date.accessioned2019-10-27T19:57:50Z
dc.date.available2019-10-27T19:57:50Z
dc.date.issued2008
dc.departmentEge Üniversitesien_US
dc.description.abstractLet K be a commutative ring with unity, R a prime K-algebra, with extended centroid C and right Utumi quotient ring U, g a non-zero generalized derivation of R. Suppose that f(x(1), . . . . ,x(n)) is a multilinear polynomial over K, I is a non-zero right ideal of R and m >= 1, a fixed integer. We prove the following results: If g(f(r(1), . . . . , r(n)))(m) = 0, for all r(1), . . . . , r(n) is an element of I, then one of the following holds: (1) [f(r(1), . . . . . , X(n)), X(n+1)] X(n+2) is an identity for I; (2) g(x) = ax for all X is an element of R, where a is an element of U such that aI = 0; (3) g(x) = ax + [q, x] for all X is an element of R, where a, q is an element of U such that aI = 0 and [q, I] I = 0. If there exist a(1), . . . , a(n) is an element of I such that g(f(a(1), . . . . , a(n)))(m) not equal 0 and g(f (r(1), . . . , r(n)))(m) is an element of Z(R), for all r(1), . . . . , r(n) is an element of I, then one of the following holds: (1) f(x(1), . . . . , x(n))x(n+1) is an identity for I; (2) f(x(1), . . . . , x(n)) is central valued on R; (3) g(x) = ax for a is an element of C and f(x(1), . . . . , x(n)) is power central valued on R; (4) R satisfies s(4), the standard identity in four variables.en_US
dc.identifier.doi10.4171/RSMUP/120-4
dc.identifier.endpage71en_US
dc.identifier.issn0041-8994
dc.identifier.issn0041-8994en_US
dc.identifier.startpage59en_US
dc.identifier.urihttps://doi.org/10.4171/RSMUP/120-4
dc.identifier.urihttps://hdl.handle.net/11454/41003
dc.identifier.volume120en_US
dc.identifier.wosWOS:000263497400004en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherC E D A M Spa Casa Editr Dott Antonio Milanien_US
dc.relation.ispartofRendiconti Del Seminario Matematico Della Universita Di Padovaen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.titleGeneralized Derivations with Power Central Values on Multilinear Polynomials on Right Idealsen_US
dc.typeArticleen_US

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