Prime Ideals and Homoderivations on Rings
Cumhuriyet Science Journal, cilt.47, sa.2, ss.350-355, 2026 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 47 Sayı: 2
- Basım Tarihi: 2026
- Doi Numarası: 10.17776/csj.1801002
- Dergi Adı: Cumhuriyet Science Journal
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.350-355
- Sivas Cumhuriyet Üniversitesi Adresli: Evet
Özet
In this paper, we aim to establish a new approach that involves characterizing the commutativity of a quotient ring ℒ/𝔓 with homoderivations of ℒ satisfying some algebraic identities involving the prime ideal 𝔓. In addition, some well-known results regarding the commutativity of prime rings have been developed for homoderivations of the rings. Some of the results obtained in this context are as follows: Let ℒ be a ring, 𝔓 a prime ideal of ℒ and 𝜉 a nonzero homoderivation of ℒ. If any one of the following holds then 𝜉(ℒ) ⊆ 𝔓 or ℒ/𝔓 is commutative integral domain: i) 𝜉([𝜇1, 𝜇2]) ∈ 𝔓, ii) 𝜉(𝜇1𝑜𝜇2) ∈ 𝔓, iii) 𝜉([𝜇1, 𝜇2]) − [𝜇1, 𝜇2] ∈ 𝔓, iv) 𝜉(𝜇1𝑜𝜇2) −𝜇1𝑜𝜇2∈ 𝔓 v) 𝜉(𝜇1𝜇2) − 𝜉(𝜇1)𝜉(𝜇2) ∈ 𝔓, vi) 𝜉(𝜇1𝜇2) −𝜉(𝜇2) 𝜉(𝜇1) ∈ 𝔓, vii) 𝜉(𝜇1) 𝜉(𝜇2) −[𝜇1, 𝜇2]∈ 𝔓, viii)𝜉(𝜇1) 𝜉(𝜇2) −𝜇1𝑜𝜇2∈ 𝔓, for all 𝜇1, 𝜇2∈ ℒ.