Search

Let (R,) be a Noetherian local ring, M a finitely generated R-module with finite projective dimension n, N an arbitrary R-module, and  be an ideal of R which is generated by s elements. In this article, we provide a surjective homomorphism from ordinary local cohomology module [image omitted] to top generalized local cohomology module [image omitted], where Pn, M is an nth syzygy of a projective resolution of M. Also, by using this epimorphism, we prove some results about the attached primes, coassociated primes, the Betti numbers, and Artinian properties of certain generalized local cohomology modules. [ABSTRACT FROM AUTHOR]

We show that the i th generalized local cohomology module of finitely generated graded modules M and N over a standard positive graded commutative Noetherian ring R , with respect to the irrelevant ideal R + , is itself graded; all its graded components are finitely generated modules over R 0 , the component of R of degree zero. Also we prove that the n th component of of this generalized local cohomology module is zero for all n ≫ 0. Moreover, in this article, we study the asymptotic behaviour of as n → -∞ in the following cases: i is the least integer j for which is not finitely generated.The base ring R 0 is local of dimension at most one and for all i ≥ 0. [ABSTRACT FROM AUTHOR]