On Generalized (Sigma,Tau)-Derivations in 3-Prime Near-Rings
Tamkang Journal of Mathematics, cilt.51, sa.1, 2020 (ESCI)
- 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.