id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2723	Shahoodh, Mohammed Khalid 	(θ1,θ2) - Derivation Pair on Rings	2022	9	.pdf	application/pdf	3918	277	92	[12] Let Γ be a ring and let 𝜇, 𝜎: Γ ⟶ Γ be two additive mappings, then 𝜇, 𝜎 are said to be derivation pair (𝜇, 𝜎) if the following equations are holds: 𝜇(𝑢𝑣𝑢) = 𝜇(𝑢)𝑣𝑢 + 𝑢𝜎(𝑣)𝑢 + 𝑢𝑣𝜇(𝑢), for each 𝑢, 𝑣 ∈ Γ 𝜎(𝑢𝑣𝑢) = 𝜎(𝑢)𝑣𝑢 + 𝑢𝜇(𝑣)𝑢 + 𝑢𝑣𝜎(𝑢), for each 𝑢, 𝑣 ∈ Γ and are called Jordan derivation pair if: 𝜇(𝑢3) Let 𝛿1, 𝛿2: Γ ⟶ Γ be additive mappings, then (𝛿1, 𝛿2) is said to be (𝜃1, 𝜃2)-derivation pair, if the following are holds: 𝛿1(𝑢𝑣𝑢) = 𝛿1(𝑢)𝜃1(𝑣𝑢) + 𝜃2(𝑢)𝛿2(𝑣)𝜃1(𝑢) + 𝜃2(𝑢𝑣)𝛿1(𝑢), for each 𝑢, 𝑣 ∈ Γ 𝛿2(𝑢𝑣𝑢) = 𝛿2(𝑢)𝜃1(𝑣𝑢) + 𝜃2(𝑢)𝛿1(𝑣)𝜃1(𝑢) + 𝜃2(𝑢𝑣)𝛿2(𝑢), for each 𝑢, 𝑣 ∈ Γ. and are said to be Jordan (𝜃1, 𝜃2)-derivation pair, if the following are holds: 𝛿1(𝑢3) = 𝛿1(𝑢)𝜃1(𝑢2) + 𝜃2(𝑢)𝛿2(𝑢)𝜃1(𝑢) + 𝜃2(𝑢2)𝛿1(𝑢) for all 𝑢 ∈ Γ Ibn Al-Haitham Jour.	cache/iajs-2723.pdf	txt/iajs-2723.txt