Article in volume
Authors:
Madhu Dadhwal
Department of Mathematics & Statistics
Himachal Predesh University
Summerhill, Shimla-171005
email: mpatial.math@gmail.com
Title:
On symmetric generalized ($\theta,\eta$)-biderivations of prime rings
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 44(1) (2024) 73-91
Received: 2022-06-28 , Revised: 2022-10-01 , Accepted: 2022-10-04 , Available online: 2024-02-08 , https://doi.org/10.7151/dmgaa.1450
Abstract:
In this paper, we characterize the actions of symmetric generalized (θ, η)-biderivations and generalized left (θ, η)-biderivations on Lie ideals and ideals of a prime ring A . It is shown that L ⊆ Z (A ), whenever traces of these derivations satisfy any of the following conditions:
(i) ([l1, l2])∆ = 0, (ii) (l1l2) ∆ ∈ Z (A ), (iii) ([l1, l2])∆ = (l1) θ ◦ (l2)∆ , (iv) (l1) ∆(l2) ∆ + (l1) η (l2) θ ∈ Z (A ), (v) a1((l1) ∆(l2) ∆ + (l1l2) θ) = 0,
(vi) (l1) ∆(l2)θ + (l1)θ(l2)∆ = 0, (vii) ([l1, l2])∆ + [(l1)∆ 24 , l2] ∈ Z (A ), (viii)[(l1l2)∆ ± (l1)θ(l2)∆ + (l1l2)θ∈ Z (A ), ∀ l1, l2 ∈ L (nonzero square-closed Lie ideal of A ), where 0 6= a1 ∈ A is a fixed element, ∆ is a trace of these biadditive mappings and θ, η are automorphisms of A .
Keywords:
Lie ideals, prime rings, generalized $(\theta,\eta)$-biderivations, generalized left $(\theta,\eta)$-biderivations
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