Derivations of higher order and commutativity of rings

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]

On 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...

Higher derivations on rings and modules

Let τ be a hereditary torsion theory on ModR and suppose that Qτ : ModR → ModR is the localization functor. It is shown that for all R-modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory. It is also shown that if τ is a TTF theory and Cτ : M →M is the colocalization functor, the...

Convergent Higher Derivations on Local Rings

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...