ON (m,n)-JORDAN DERIVATIONS AND COMMUTATIVITY OF PRIME RINGS
نویسندگان
چکیده
منابع مشابه
On derivations and commutativity in prime rings
Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R, and I a nonzero right ideal of R such that [[d(x), x], [d(y), y]] = 0, for all x, y ∈ I. We prove that if [I, I]I ≠ 0, then d(I)I = 0. 1. Introduction. Let R be a prime ring and d a nonzero derivation of R. Define [x, y] 1 = [x, y] = xy − yx, then an Engel condition is a polynomial [x, y] k = [[x, y] k−1 ,y]
متن کاملOn Generalized Derivations and Commutativity of Prime Rings with Involution
Let R be a ring with involution ′∗′. A map δ of the ring R into itself is called a derivation if δ(xy) = δ(x)y + xδ(y) for all x, y ∈ R. An additive map F : R → R is called a generalized derivation on R if F(xy) = F(x)y + xδ(y) for all x, y ∈ R, Permanent address: Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh202002, India 292 Shakir Ali and Husain Alhazmi whe...
متن کاملCentralizing automorphisms and Jordan left derivations on σ-prime rings
Let R be a 2-torsion free σ-prime ring. It is shown here that if U 6⊂ Z(R) is a σ-Lie ideal of R and a, b in R such that aUb = σ(a)Ub = 0, then either a = 0 or b = 0. This result is then applied to study the relationship between the structure of R and certain automorphisms on R. To end this paper, we describe additive maps d : R −→ R such that d(u) = 2ud(u) where u ∈ U, a nonzero σ-square close...
متن کاملOn Jordan left derivations and generalized Jordan left derivations of matrix rings
Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...
متن کاملTwo Torsion Free Prime Gamma Rings With Jordan Left Derivations
Let M be a 2-torsion free prime Γ-ring and X a nonzero faithful and prime ΓM -module. Then the existence of a nonzero Jordan left derivation d : M → X satisfying some appropriate conditions implies M is commutative. M is also commutative in the case that d : M → M is a derivation along with some suitable assumptions. AMS (MOS) Subject Classification Codes: 03E72, 54A40, 54B15
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Demonstratio Mathematica
سال: 2008
ISSN: 2391-4661
DOI: 10.1515/dema-2008-0405