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Original scientific paper

https://doi.org/10.3336/gm.47.1.08

On (anti-)multiplicative generalized derivations

Daniel Eremita ; Department of Mathematics and Computer Science, FNM, University of Maribor, 2000 Maribor, Slovenia
Dijana Ilisevic orcid id orcid.org/0000-0002-0833-3016 ; Department of Mathematics, University of Zagreb, Bijenička 30, P.O.Box 335, 10002 Zagreb, Croatia


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Abstract

Let R be a semiprime ring and let F, f : R → R be (not necessarily additive) maps satisfying F(xy)=F(x)y+xf(y) for all x,y R. Suppose that there are integers m and n such that F(uv)=mF(u)F(v)+nF(v)F(u) for all u, v in some nonzero ideal I of R. Under some mild assumptions on R, we prove that there exists c C(I⊥⊥) such that c=(m+n)c2, nc[I⊥⊥, I⊥⊥]=0 and F(x)=cx for all x I⊥⊥. The main result is then applied to the case when F is multiplicative or anti-multiplicative on I.

Keywords

Additivity, ring, semiprime ring, prime ring, derivation, generalized derivation, homomorphism, anti-homomorphism

Hrčak ID:

82574

URI

https://hrcak.srce.hr/82574

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