Linear growth of primary decompositions of modules and integral closures

CIMEN N., Erdogan A., TIRAS Y.

COMMUNICATIONS IN ALGEBRA, vol.30, no.9, pp.4605-4611, 2002 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 9
  • Publication Date: 2002
  • Doi Number: 10.1081/agb-120013341
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4605-4611
  • Hacettepe University Affiliated: Yes

Abstract

Let R be a commutative Noetherian ring with identity. I. Swanson proved in([10]) that every ideal in every commutative Noetherian ring has linear growth of primary decompositions. Later, in([8]), R.Y. Sharp generalized this result to finitely generated modules over R. In the first section we present another (may be simpler) proof of this generalized result. Sharp also proved in([7]) that every proper ideal in R has linear growth of primary decompositions for integral closures of ideals. We extend, in the last section, this result to finitely generated modules over R.