Affiliation:
1. KOCAELİ ÜNİVERSİTESİ, FEN EDEBİYAT FAKÜLTESİ
Abstract
Assume we have a prime ring denoted as $R$, with a characteristic distinct from two. The concept of a homoderivation refers to an additive map $Η$ of a ring $R$ that satisfies the property $Η(r_1 r_2 )=Η(r_1 ) r_2+r_1 Η(r_2 )+Η(r_1 )Η(r_2 )$, $\forall r_1,r_2 \in R$. This article aims to obtain results for prime rings, ideals, and Lie ideals by utilizing the concept of homoderivation in conjunction with the established theory of derivations.
Publisher
Izmir Democracy University
Subject
General Earth and Planetary Sciences,General Environmental Science
Reference18 articles.
1. 1. Alharfie E. F., Muthana N. M. (2018). The commutativity of prime rings with homoderivations, Int. J. of Adv. and App. Sci., 5(5), 79-81.
2. 2. Awtar R. (1984). Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc., 90, 1, 9-14.
3. 3. Atteya M. J. (2022). Homogeneralized (σ,τ)-Derivations of Associative Rings, Studies on Scientific Developments in Geometry, Algebra, and Applied Mathematics, 52.
4. 4. Bergen J., Herstein I. N., Kerr J. (1981). Lie Ideals and derivations of Prime Rings, Journal of Algebra, 71, 259-267.
5. 5. Divinsky N. (1965). Rings and Radicals, University of Toronto Press, Toronto.