ABSOLUTE CO-SUPPLEMENT AND ABSOLUTE CO-COCLOSED MODULES

Tutuncu D. K., Toksoy S. E.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.42, sa.1, ss.67-79, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 1
  • Basım Tarihi: 2013
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.67-79
  • Hacettepe Üniversitesi Adresli: Evet

Özet

A module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M congruent to T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0 -> A -> B -> C -> 0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.