Document Type : Original Article
Authors
1 Erbil polytechnic university
2 Mathematics Department, College of Basic Education, Salahaddin University, Erbil, Kurdistan Region, Iraq
Abstract
It is our intention in this research generalize some concept in local cohomology such as free modules, contravariant functor $ext$, covariant functor $Ext$ and ideal transforms with $e$-exact sequences. The $e$-exact sequence was introduced by Akray and Zebari \cite{AZ} in 2020. we prove that essential free module is an essential projective and a submodule $rM$ of $M$ is a quotient of essential free modules. Furthermore, we obtain that for a torsion-free modules $B$, $_eex^n_R(P,B)=0$ while $_eExt^n_R(A,E)=0$ for every module $A$. Also for any torsion-free modules we have an $e$-exact sequence $0\to \Gamma_{a}(B) \to B\to D_{a}(B)\to H^1_{a}(B)\to 0$ 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.
Keywords
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