Essential ideal transforms

Runak H. Mustafa; Ismael Akray

paper

Essential ideal transforms

arXiv:2309.10442

Abstract

It is our intention in this research generalized some concept in local cohomology such as contravarint functor $e x t$ , covariant functor $E x t$ , covarian functor $T or$ and ideal transforms with $e$ -exact sequences. The $e$ -exact sequence was introduced by Akray and Zebari \cite{AZ} in 2020. We obtain for a torsion-free modules $B$ , $_{e} e x t_{R}^{n} (P, B) = 0$ while $_{e} E x t_{R}^{n} (A, E) = 0$ for every module $A$ . Also for any torsion-free module $B$ we have an $e$ -exact sequence $0 \to Γ_{a} (B) \to B \to D_{a} (B) \to H_{a}^{1} (B) \to 0$ and an isomorphisms between $B$ and $r D_{a} (B)$ . Finally we generalize Mayer-Vietories with $e$ -exact sequences in essential local cohomology, we get a special $e$ -exact sequences.