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- Title
Engel type identities with generalized derivations in prime rings.
- Authors
Dhara, Basudeb; Pradhan, Krishna Gopal; Tiwari, Shailesh Kumar
- Abstract
Let R be a noncommutative prime ring with its Utumi ring of quotients U , C = Z ( U ) the extended centroid of R , G a generalized derivation of R and I a nonzero ideal of R. If I satisfies any one of the following conditions: (i) [ [ G ( [ x , y ] n ) , [ x , y ] n ] , G ( [ x , y ] n ) ] ∈ C , (ii) ( G ( x ∘ n y ) ∘ ( x ∘ n y ) ) ∘ G ( x ∘ n y ) ∈ C , where n ≥ 1 is a fixed integer, then one of the following holds: (1) there exists λ ∈ C such that G ( x ) = λ x for all x ∈ R ; (2) R satisfies s 4 and there exist a ∈ U and λ ∈ C such that G ( x ) = a x + x a + λ x for all x ∈ R ; (3) char ( R ) = 2 , R satisfies s 4 and there exist λ ∈ C and an outer derivation d of R such that G ( x ) = λ x + d ( x ) for all x ∈ R.
- Subjects
ENGEL'S law; COMMUTATIVE rings; QUOTIENT rings; POLYNOMIAL rings; PERMUTATION groups; LIE algebras
- Publication
Asian-European Journal of Mathematics, 2018, Vol 11, Issue 4, pN.PAG
- ISSN
1793-5571
- Publication type
Article
- DOI
10.1142/S1793557118500559