Article

A note on graded generalized local cohomology modules

Published in: Quaestiones Mathematicae
Volume 40 , issue 5 , 2017 , pages: 599–604

DOI: 10.2989/16073606.2017.1303005

Author(s): Hero Saremi Department of Mathematics, Iran

Keywords: 13D45 , 13A02 , 13E10 , 13D45 , 13A02 , 13E10

Abstract

Let be a positively graded commutative Noetherian ring with irrelevant ideal and let ɑ be a graded ideal contained in R₊. Let M, N be two finitely generated graded R-modules. In this paper, we study the finiteness and vanishing of the n-th graded component of the i-th generalized local cohomology module of M and N with respect to ɑ. Also, we show that the least i such that is equal to the least integer i for which is not finitely graded, where a graded module is finitely graded which is non-zero in only finitely many graded pieces.

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