• ORTHOGONALITY OF (𝛔, 𝛕)-DERIVATIONS AND BI-(𝛔, 𝛕)-DERIVATIONS IN SEMIPRIME RINGS
Abstract
This paper gives the notion of orthogonality between (s,t)-Derivations and Bi-(s,t)-Derivations in Semiprime rings. In this paper, we give three conditions equivalent to the notion of orthogonality between the (s,t)-derivation and bi-(s,t)-derivation of a semiprime ring. It is shown that if R is a 2-torsion free semiprime ring, B is a bi-(s,t)-derivation and d is a (s,t)-derivation on R, then B and d are orthogonal if only if one of the following equivalent conditions holds for every : (i) dB=0 (ii) or (iii) dB is a bi- (s,t)-derivation
Keywords
Semiprime ring, Derivation, Biderivation, Orthogonal, (𝛔, 𝛕)-Derivation and Bi-(𝛔, 𝛕)-Derivations.
Full Text:
PDFThis work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
© 2010-2022 International Journal of Mathematical Archive (IJMA) Copyright Agreement & Authorship Responsibility |