ASYMPTOTIC BEHAVIOR OF INTEGRAL CLOSURES, QUINTASYMPTOTIC PRIMES AND IDEAL TOPOLOGIES

作者：Naghipour Reza^*; Schenzel Peter

来源：Rocky Mountain Journal of Mathematics, 2018, 48(2): 551-572.

DOI：10.1218/RMJ-2018-48-2-551

• Integral closure
• ideal topologies
• local cohomology
• quintasymptotic prime

Let R be a Noetherian ring, N a finitely generated R-module and I an ideal of R. It is shown that the sequences Ass(R) R/(I-n)(a)((N)), AssR (I-n)a((N))/(In+1)a((N) )and AssR (I-n)a((N))/(I-n)(a), n = 1, 2, ..., associated prime ideals, are increasing and ultimately constant for large n. Moreover, it is shown that, if S is a multiplicatively closed subset of R, then the topologies defined by (I-n)(a)((N) )and S((I-n)(a)(N), n >= 1, are equivalent if and only if S is disjoint from the quintasymptotic primes of I. By using this, we also show that, if (R,m) is local and N is quasi-unmixed, then the local cohomology module H-I(dim) (N )(N) vanishes if and only if there exists a multiplicatively closed subset S of R such that m boolean AND S not equal empty set and the topologies induced by (I-n)(a)((N) )and S((I-n)(a)((N)), n >= 1, are equivalent.

• 出版日期2018