A basic functional identity with applications to Jordan σ-biderivations. Issue 4 (3rd April 2017)

• Record Type: Journal Article
• Authors: Abdioğlu, Cihat; Lee, Tsiu-Kwen
• Is Part Of: Communications in algebra. Volume 45:Issue 4(2017)
• Page Start: 1741
• Page End: 1756
• Publication Date: 2017-04-03
• Subjects: Extended centroid -- functional identity -- Jordan (bi-)derivation -- matrix ring -- prime ring; 16R60 -- 16W10 -- 16W25 -- 16N60; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1222413
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let R be a noncommutative prime ring with extended centroid C and maximal left ring of quotients Q ml ( R ). The aim of the paper is to study a basic functional identity concerning bi-additive maps on R . Precisely, it is proved that a bi-additive map B : R × R → Q ml ( R ) satisfying [ B ( x, y ), [ x, y ]] = 0 for all x, y ∈ R must be of the form ( x, y )↦λ[ x, y ]+ μ ( x, y ) for x, y ∈ R, where λ∈ C and μ : R × R → C is a bi-additive map. As applications to the theorem, Jordan σ -biderivations with σ an epimorphism and additive commuting maps on noncommutative Lie ideals of R are characterized.