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

Koç Sögütcü E.

Tamkang Journal of Mathematics, cilt.51, sa.1, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.5556/j.tkjm.51.2020.1829
  • Dergi Adı: Tamkang Journal of Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Anahtar Kelimeler: Near-rings, semigroup ideal, (sigma, tau)-derivation, generalized (sigma, tau)-derivation, DERIVATIONS
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

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.