Some Results on the Finiteness of Generalized Local Cohomology Modules Using Serre Classes

Let R be a commutative Noetherian ring with identity and a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak{a}$$\end{document} be an ideal of R. In this paper, we investigate the conditions under which the set of associated primes of generalized local cohomology modules is finite. For this aim, we study some relations between generalized local cohomology modules, ideal transform, Ext and ordinary local cohomology modules in the Serre classes of R-modules. Such relations provided a common language for expressing some results about the generalized local cohomology R-modules, that has appeared in some papers.