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Generalized Skew Derivations Implemented by Elementary Operators |
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| Authors: | Daniel Eremita Ilja Gogi? Dijana Ili?evi? |
| Institution: | 1. Department of Mathematics and Computer Science, FNM, University of Maribor, 2000, Maribor, Slovenia 2. Department of Mathematics, University of Zagreb, Bijeni?ka 30, 10000, Zagreb, Croatia 3. Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovi?a 4, 21000, Novi Sad, Serbia |
| Abstract: | Let R be a semiprime ring with the maximal right ring of quotients Q mr . An additive map d: R →Q mr is called a generalized skew derivation if there exists a ring endomorphism σ:R →R and a map \(\d:R \to Q_{mr}\) such that \(d(xy)=\d(x)y+\sigma(x)d(y)\) for all x,y?∈?R. If σ is surjective, we determine the structure of generalized skew derivations for which there exists a finite number of elements a i ,b i ?∈?Q mr such that d(x)?=?a 1 xb 1?+???+?a n xb n for all x?∈?R. |
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