Open AccessDifferential identities in prime rings
Author(s) -
Abdelkarim Boua,
Ahmed Y. Abdelwanis
Publication year - 2021
Publication title -
mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.294
H-Index - 6
eISSN - 2601-744X
pISSN - 1222-9016
DOI - 10.24193/mathcluj.2021.2.06
Subject(s) - automorphism , prime (order theory) , prime ring , mathematics , alpha (finance) , ring (chemistry) , center (category theory) , pure mathematics , characterization (materials science) , beta (programming language) , commutative ring , algebra over a field , combinatorics , commutative property , computer science , physics , construct validity , statistics , chemistry , programming language , organic chemistry , optics , crystallography , psychometrics
Let R be a prime ring with center Z(R) and alpha,beta be automorphisms of R. This paper is divided into two parts. The first tackles the notions of (generalized) skew derivations on R, as the subject of the present study, several characterization theorems concerning commutativity of prime rings are obtained and an example proving the necessity of the primeness hypothesis of R is given. The second part of the paper tackles the notions of symmetric Jordan bi (alpha,beta)-derivations. In addition, the researchers illustrated that for a prime ring with char(R) different from 2, every symmetric Jordan bi (alpha,alpha)-derivation D of R is a symmetric bi (alpha,alpha)-derivation.