Vietnam Journal of Mathematics 33:2 (2005)
214-221
When M-Cosingular Modules Are Projective
Derya Keskin Tütüncü
and Rachid Tribak
Abstract. Let M be an R-module. Talebi
and Vanaja investigate the category σ[M] such that every M-cosingular
module in σ[M] is projective
in σ[M]. In the light of
this property we call M a
COSP-module if every M-cosingular
module is projective in σ[M].
This note is devoted to the investigation of these classes of modules. We
prove that every COSP-module is a coatomic module having a semisimple
radical. We also characterise COSP-module when every injective module in
σ[M] is amply supplemented.
Finally we obtain that a COSP-module is artinian if and only if every
submodule has finite hollow dimension.
Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
