منابع مشابه
A 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 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 کاملAdditivity of Jordan Elementary Maps on Rings
We prove that Jordan elementary surjective maps on rings are automatically additive. Elementary operators were originally introduced by Brešar and Šerml ([1]). In the last decade, elementary maps on operator algebras as well as on rings attracted more and more attentions. It is very interesting that elementary maps and Jordan elementary maps on some algebras and rings are automatically additive...
متن کاملLahcen Oukhtite GENERALIZED JORDAN LEFT DERIVATIONS IN RINGS WITH INVOLUTION
In the present paper we study generalized left derivations on Lie ideals of rings with involution. Some of our results extend other ones proven previously just for the action of generalized left derivations on the whole ring. Furthermore, we prove that every generalized Jordan left derivation on a 2-torsion free ∗-prime ring with involution is a generalized left derivation.
متن کاملA Note on Jordan∗− Derivations in Semiprime Rings with Involution
In this paper we prove the following result. Let R be a 6−torsion free semiprime ∗−ring and let D : R → R be an additive mapping satisfying the relation D(xyx) = D(x)y∗x∗ + xD(y)x∗ + xyD(x), for all pairs x, y ∈ R. In this case D is a Jordan ∗−derivation. Mathematics Subject Classification: 16W10, 39B05
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1979
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1979-0531985-4