The torsion theory generated by M-small modules

Ozcan A. Ç. , HARMANCI A.

ALGEBRA COLLOQUIUM, vol.10, no.1, pp.41-52, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 1
  • Publication Date: 2003
  • Doi Number: 10.1007/s100110300006
  • Title of Journal : ALGEBRA COLLOQUIUM
  • Page Numbers: pp.41-52


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.