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 HsHomRPnM N to top generalized local cohomology module Hn+s M N, where PnM 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.
