On Generalized (Sigma,Tau)-Derivations in 3-Prime Near-Rings


Koç Sögütcü E.

Tamkang Journal of Mathematics, vol.51, no.1, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.5556/j.tkjm.51.2020.1829
  • Journal Name: Tamkang Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index, Scopus, zbMATH
  • Keywords: Near-rings, semigroup ideal, (sigma, tau)-derivation, generalized (sigma, tau)-derivation, DERIVATIONS

Abstract

Let N be a 2-torsion free 3-prime left near-ring with multiplicative center Z, I be a nonzero semigroup ideal of N and f be a right generalized (sigma, tau)-derivation on N associated with a (sigma, tau)-derivation d. Assume d sigma = sigma d, d tau = tau d, f sigma = sigma f, f tau = tau f. We prove that N is a commutative ring or d = 0 if any one of the following holds: i) f(N) subset of Z ii) f(I) subset of Z. Moreover, if f is a generalized (sigma, tau) derivation on N associated with d, then d = 0 if any one of the following is satisfied : iii) f acts as a homomorphism on I iv) f acts as an anti-homomorphism on I.