Cocentralizing generalized derivations on multilinear polynomial on right ideals of prime rings

• Autorzy: Filippis V. de , Dhara B.
• Języki publikacji: EN

Abstrakty

EN

Let R be a prime ring with Utumi quotient ring U and with extended centroid C, I a non-zero right ideal of R, f(x1,…,xn) a multilinear polynomial over C which is not central valued on R and G, H two generalized derivations of R. Suppose that G(f(r))f(r) – f(r)H(f(r)) € C, for all r = (r1,…,rn) € In. Then one of the following holds: 1. there exist a; b; p (…) ; 2. R satisfies s4, the standard identity of degree 4, and there exist a; (…) ; 3. R satisfies s4 and there exist a; (…) ; 4. R satisfies s4 and there exist a; (…) ; 5. there exists e2 = e (…) and one of the following holds: (a) (…) is an identity for I; (b) char(R) = 2 and s4(x1, x2, x3, x4)x5 is an identity for I; (c) (…) is an identity for I and there exist a, a’, b, b’ (…) , a derivation of R, such that G(x) = ax + xa’ + d(x), H(x) = bx + xb’ – d(x), for all x (…) R, with (a – b’ – α)I = (0) = (b – a’ – α)I.

Słowa kluczowe

EN

prime rings; differential identities; generalized derivation

PL

pierścienie pierwszorzędowe; tożsamość różniczkowa; pochodna uogólniona

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 1
• Strony: 22--36
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Filippis V. de

• University of Messina 98166, Messina, Italy

autor

Dhara B.

• Department of Mathematics Belda College Belda, Paschim Medinipur-721424, India

Bibliografia

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