2005/02/03 by Kamran Divaani-Aazar, Амир Мафи, Divaani-Aazar, Kamran +1
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Topological and Geometric Data Analysis #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.math/0502074
The notion of weakly Laskerian modules was introduced recently by the\nauthors. Let R be a commutative Noetherian ring with identity, fa an ideal\nof R, and M a weakly Laskerian module. It is shown that if fa is\nprincipal, then the set of associated primes of the local cohomology module\nH fai(M) is finite for all i\≥ 0. We also prove that when R is\nlocal, then AssR(H fai(M)) is finite for all i\≥ 0 in the following\ncases: (1) \dim R\≤ 3, (2) \dim R/ fa\≤ 1, (3) M is Cohen-Macaulay\nand for any ideal fb, with l= grade( fb,M),\n HomR(R/ fb,H fbl+1(M)) is weakly Laskerian.\n