Strongly 0-dimensional Modules

Oral K. H., ÖZKİRİŞCİ N. A., TEKİR Ü.

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, cilt.57, sa.1, ss.159-165, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 57 Sayı: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.4153/cmb-2013-004-3
  • Dergi Adı: CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.159-165
  • Anahtar Kelimeler: Strongly 0-dimensional rings, Q-module, Von Neumann regular module, SUBMODULES
  • Marmara Üniversitesi Adresli: Evet

Özet

In a multiplication module, prime submodules have the following property: if a prime submodule contains a finite intersection of submodules, then one of the submodules is contained in the prime submodule. In this paper, we generalize this property to infinite intersection of submodules and call such prime submodules strongly prime submodules. A multiplication module in which every prime submodule is strongly prime will be called a strongly 0-dimensional module. It is also an extension of strongly 0-dimensional rings. After this we investigate properties of strongly 0-dimensional modules and give relations of von Neumann regular modules, Q-modules and strongly 0-dimensional modules.