id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5948	Al-Omary, Radwan M; Hummdi, Ali Yahya ; Al-Amery, Zakia Zaid 	Specific Identities Involving Prime Ideals with Generalized $P$-derivations	2025	12	.pdf	application/pdf	6274	327	75	̸= 2, where P is a prime ideal of ℜ. Building on these previous findings, it is natural to inquire about the situation of a factor ring ℜ/P when ℜ admits generalized P -derivations (℧, χ) and (⨿,∝) that satisfy the identity [υ,⨿(℘)] ± ℧([υ, ℘]) ∈ P for all υ, ℘ ∈ ℜ. To address this question, we will now present the following theorem. Let ℜ be a ring equipped with a generalized P -derivation (℧, χ) such that ℧([υ, ℘])±([υ, ℘]) ∈ P for all υ, ℘ ∈ ℜ. Then ℜ/P is an integral domain or (℧±idℜ)(ℜ) ⊆ P .	cache/ejpam-5948.pdf	txt/ejpam-5948.txt