On non Artinian cofinite generalized local cohomology modules

Abstract

Let $R$ be a commutative Noetherian ring and $I\subseteq J$ be ideals of $R$. Let $M$ and $N$ be finitely generated $R$-modules such that . In this paper, we study the supremum of non Artinian $I$-cofinite modules $H_I^i(M,N)$ over a commutative Noetherian ring where $i\ge 1$ and give a bound for ${\tilde{\text{q}}}_J(M,N)$ by using ${\tilde{\text{q}}}_I(M,N)$. We show that ${\tilde{\text{q}}}_J(M,N)\le {\tilde{\text{q}}}_I(M,N)+{\text{cd}}_J(M,N/IN)$.