Functional identities of degree 2 vanishing on zero products of XY and Y X
Articles > Article · 2021
Authors: Nefıse Cezayırlıoğlu, Çağri Demır
Linear and Multilinear Algebra, International, WoS, 2021, vol 70, pp 4876-4896
DOI: 10.1080/03081087.2021.1900050
Summary
Let R be a unitary prime ring with the maximal left ring of quotients Qml(R). We completely characterize the forms of additive maps F1,F2,G1,G2:R→Qml(R) such that F1(x)y+F2(y)x+xG1(y)+yG2(x)=0whenever x,y∈R satisfy xy = 0 = yx under the assumptions that R contains a nontrivial idempotent and characteristic of R is not 2. This partially generalizes a result of T.K. Lee in [Bi-additive maps of ζ-Lie product type vanishing on zero products of XY and Y X. Comm Algebra. 2017;45(8):3449–3467].