Öz
In this paper we introduce and investigate M-cofaithful modules. A
module N ∈ σ[M] is called M-cofaithful if for every $0\neq$ f ∈ HomR(N,X) with X ∈ σ[M], Hom$_R(X,M)f \neq 0$. We show that if N
is an M-cofaithful weak supplemented module and HomR(N, M) a noetherian S-module, then there exists an order-preserving correspondence
between the coclosed R-submodules of N and the closed S-submodules of HomR(N,M), where S = EndR(M). Some applications are: (1) the
,connection between M's being a lifting module and EndR(M)'s being
an extending ring; (2) the equality between the hollow dimension of a
quasi-injective coretractable module M and the uniform dimension of
EndR(M).
Anahtar Kelimeler
M-Cofaithful modules Coretractable modules Closed and coclosed submodules
Kaynakça
- .
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Aralık 2015 |
| Yayımlandığı Sayı | Yıl 2015 Cilt: 44 Sayı: 6 |