Bi-additive maps of ξ-Lie product type vanishing on zero products of XY and YX. Issue 8 (3rd August 2017)

• Record Type: Journal Article
• Authors: Lee, Tsiu-Kwen
• Is Part Of: Communications in algebra. Volume 45:Issue 8(2017)
• Page Start: 3449
• Page End: 3467
• Publication Date: 2017-08-03
• Subjects: Bi-additive map -- functional identity -- idempotent -- maximal left ring of quotients -- prime ring -- ξ-Lie product -- zero-product preserving; 16R60 -- 16W25 -- 16N60; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1236937
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: We study bi-additive maps of ξ -Lie product type satisfying certain local property from the viewpoint of functional identities. Let R be a unital prime ring with extended centroid C, ξ ∈ C, and maximal left ring of quotients Q ml ( R ). Suppose that R contains a nontrivial idempotent. We completely characterize additive maps ϕ : R → Q ml ( R ) having the property that[ ϕ ( x ), y ] ξ + [ x, ϕ ( y ) ] ξ = 0 whenever x, y ∈ R satisfy xy = 0 = yx . As consequences, some known results are fully generalized.