The torsion theory generated by M-small modules

Ozcan A. Ç., HARMANCI A.

ALGEBRA COLLOQUIUM, cilt.10, sa.1, ss.41-52, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 1
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1007/s100110300006
  • Dergi Adı: ALGEBRA COLLOQUIUM
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.41-52
  • Hacettepe Üniversitesi Adresli: Evet

Özet

Let M be a right R-module, M the class of all M-small modules, and P a projective cover of M in sigma[M]. We consider the torsion theories tau(M) = (TM,.FM), tauv = (Tv, Fv), and taup = (Tp, Fp) in sigma[M], where tau(M) is the torsion theory generated by M, tauv is the torsion theory cogenerated by M, and taup is the dual Lambek torsion theory. We study some conditions for tau(M) to be cohereditary, stable, or split, and prove that Rej (M, M) = M double left right arrow Fp = M (= TM = Fv) double left right arrow Tp = Tv Gen(M) (P) subset of or equal to Tv.