Akademik Veri Yönetim Sistemi
Natural and Applied Sciences Journal, cilt.6, sa.1, ss.41-49, 2023 (Hakemli Dergi)
In this paper, properties of the ideal 𝐼 of semiprime ring 𝑅 with multiplicative generalized (𝛼, 𝛽) − reverse derivation with determined not necessarily additive map 𝑑 is studied. We generalized previous studies for different derivations to multiplicative generalized (𝛼, 𝛽) − reverse derivation 𝐹. We show that [𝛽(𝑝), 𝑑(𝑝)]𝐼 = 0 for all 𝑝 ∈ 𝐼 or [𝑑(𝑝)], 𝛼(𝑝)]𝐼 = 0 for all 𝑝 ∈ 𝐼 under the given different conditions. Also, we give the relationship between map 𝑑 and anti-automorphism 𝛼 of semiprime ring 𝑅 and automorphism 𝛽 of semiprime ring 𝑅. Under the given different conditions, we examine whether 𝑑 is 𝛼 − commuting on ideal 𝐼 or 𝛽 − commuting on ideal 𝐼 and obtain new results.