Southeast Asian Bulletin of Mathematics c  SEAMS. 2009 Southeast Asian Bulletin of Mathematics (2009) 33: 885–889 Associated Primes of the Top Local Homology Modules with Respect to Maximal Ideal * Amir Mafi University of Kurdistan, Pasdaran ST., P.O. Box: 416, Sanandaj, Iran and School of Mathematics, Institute for Research in Fundamental Science (IPM), P.O. Box 19395- 5746, Tehran, Iran E-mail: a-mafi@araku.ac.ir Received 6 December 2006 Accepted 26 July 2007 Communicated by Nguyen Van Sanh AMS Mathematics Subject Classification (2000): 13C14, 13C15, 13E10 Abstract. Let (R, m) be a Noetherian local ring and M a non-zero, Artinian R-module of dimension d. In this paper, we study the associated primes of the top local homology module H m d (M). Keywords: Local homology modules; Noetherian dimension; Artinian modules. 1. Introduction Throughout this paper, we assume that (R, m) is a commutative Noetherian local ring and M an Artinian R-module. For an ideal a of R, the i-th local homology module of M with respect to a is defined as H a i (M ) = lim ←- n Tor R i (R/a n ,M ). The reader is referred to [1], [2], [13] and [14] for the definitions and basic results about local homology. As is well-known, this definition is dual to Grothendieck’s definition of local cohomology modules for finitely generated modules over Noe- therian rings (see [5]). * This research was partially supported by a grant from IPM (No. 86130029).