Certain basic functional identities of semiprime rings
Journal
Communications in Algebra
Journal Volume
47
Journal Issue
1
Pages
17-29
Date Issued
2019
Author(s)
Abstract
The goal of the article is to discuss certain basic functional identities of semiprime rings. Specifically, the following result is proved: Let R be a semiprime ring with extended centroid C and let f,g:R→Qml(R) be additive maps, where Qml(R) denotes the maximal left ring of quotients of R. Suppose that f(x)x+xg(x)∈C for all x∈R. Then there exist b∈Qml(R),β∈C and additive maps ν,η:R→C such that f(x)=xb+ν(x) and g(x)=(−b+β)x+η(x) for all x∈R. Moreover, some related functional identities are also characterized.
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