On Jordan left-I-centralizers of prime and semiprime gamma rings with involution
نویسندگان
چکیده
منابع مشابه
On centralizers of prime rings with involution
Let $R$ be a ring with involution $*$. An additive mapping $T:Rto R$ is called a left(respectively right) centralizer if $T(xy)=T(x)y$ (respectively $T(xy)=xT(y)$) for all $x,yin R$. The purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.
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 کاملCentralizers 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 centralizers of prime rings with involution
let $r$ be a ring with involution $*$. an additive mapping $t:rto r$ is called a left(respectively right) centralizer if $t(xy)=t(x)y$ (respectively $t(xy)=xt(y)$) for all $x,yin r$. the purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.
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.
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ژورنال
عنوان ژورنال: Journal of the Egyptian Mathematical Society
سال: 2016
ISSN: 1110-256X
DOI: 10.1016/j.joems.2014.08.002