An identity related to centralizers in semiprime rings
نویسنده
چکیده
The purpose of this paper is to prove the following result: Let R be a 2torsion free semiprime ring and let T : R → R be an additive mapping, such that 2T (x) = T (x)x + xT (x) holds for all x ∈ R. In this case T is left and right centralizer.
منابع مشابه
Centralizers on prime and semiprime rings
The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let R be a noncommutative prime ring of characteristic different from two and let S and T be left centralizers on R. Suppose that [S(x), T (x)]S(x) + S(x)[S(x), T (x)] = 0 is fulfilled for all x ∈ R. If S 6= 0 (T 6= 0) then there exists λ from the extende...
متن کاملOn Θ-centralizers of Semiprime Rings (ii)
The following result is proved: Let R be a 2-torsion free semiprime ring, and let T : R → R be an additive mapping, related to a surjective homomorphism θ : R → R, such that 2T (x2) = T (x)θ(x) + θ(x)T (x) for all x ∈ R. Then T is both a left and a right θ-centralizer.
متن کاملCentralizers on semiprime rings
The main result: Let R be a 2-torsion free semiprime ring and let T : R → R be an additive mapping. Suppose that T (xyx) = xT (y)x holds for all x, y ∈ R. In this case T is a centralizer.
متن کاملA Note on Jordan Left ∗-Centralizers in Rings with Involution
Let R be a ring with involution. An additive mapping T : R → R is called a left ∗-centralizer (resp. Jordan left ∗-centralizer) if T (xy) = T (x)y∗ (resp. T (x2) = T (x)x∗) holds for all x, y ∈ R, and a reverse left ∗-centralizer if T (xy) = T (y)x∗ holds for all x, y ∈ R. The purpose of this paper is to solve some functional equations involving Jordan left ∗-centralizers on some appropriate su...
متن کاملCharacterization of $delta$-double derivations on rings and algebras
The main purpose of this article is to offer some characterizations of $delta$-double derivations on rings and algebras. To reach this goal, we prove the following theorem:Let $n > 1$ be an integer and let $mathcal{R}$ be an $n!$-torsion free ring with the identity element $1$. Suppose that there exist two additive mappings $d,delta:Rto R$ such that $$d(x^n) =Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+Si...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010