Factor Rings with Algebraic Identities via Generalized Derivations - Ali Yahya Hummdi; Zakia Z. Al-Amery; Radwan M. Al-omary (Axioms)
The current article focuses on studying the behavior of a ring <semantics>ℜ/Π</semantics> when ℜ admits generalized derivations <semantics>Ψ</semantics> and <semantics>Ω</semantics> with associated derivations <semantics>ϕ</semantics> and <semantics>δ</semantics>, respectively. These derivations satisfy specific differential identities involving <semantics>Π</semantics>, where <semantics>Π</semantics> is a prime ideal of an arbitrary ring ℜ, not necessarily prime or semiprime. Furthermore, we explore some consequences of our findings. To emphasize the necessity of the primeness of <semantics>Π</semantics> in the hypotheses of our various theorems, we provide a list of examples.