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Asymptotic Primes of Ratliff–Rush Closure of Ideals with Respect to Modules
2008
Communications in Algebra
This is a joint work with R. Naghipour. Let R be a commutative Noetherian ring, M a non-zero finitely generated R-module and I an ideal of R. The purpose of this paper is to develop the concept of Ratliff-Rush closure I (M ) of I with respect to M . It is shown that the sequence Ass R R/ I n (M ) , n = 1, 2, ..., of associated prime ideals is increasing and eventually stabilizes. This result extends Mirbagheri-Ratliffs main result in On the relevant transform and the relevant component of an
doi:10.1080/00927870801941689
fatcat:xxsyquzak5drxdzidjlhej5cbi