Linear growth of primary decompositions of modules and integral closures

CIMEN N., Erdogan A., TIRAS Y.

COMMUNICATIONS IN ALGEBRA, cilt.30, sa.9, ss.4605-4611, 2002 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 9
  • Basım Tarihi: 2002
  • Doi Numarası: 10.1081/agb-120013341
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4605-4611
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.