Dedekind modules

Alkan M., Saraç B., Tıraş Y.

COMMUNICATIONS IN ALGEBRA, cilt.33, sa.5, ss.1617-1626, 2005 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 5
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1081/agb-200061007
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1617-1626
  • Anahtar Kelimeler: Dedekind modules and Dedekind domains, integrally closed, invertible submodules, MULTIPLICATION MODULES, DENSE SUBMODULES
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, the authors introduce the concept of integrally closed modules and characterize Dedekind modules and Dedekind domains. They also show that a given domain R is integrally closed if and only if a finitely generated torsion-free projective R-module is integrally closed. In addition, it is proved that any invertible submodule of a finitely generated projective module over a domain is finitely generated and projective. Also they give the equivalent conditions for Dedekind modules and Dedekind domains.