Öz
We examine the properties of certain mappings between the lattice
L(R) of ideals of a commutative ring R and the lattice L(RM) of submodules
of an R-module M, in particular considering when these mappings are complete
homomorphisms of the lattices. We prove that the mapping λ from L(R)
to L(RM) defined by λ(B) = BM for every ideal B of R is a complete homomorphism
if M is a faithful multiplication module. A ring R is semiperfect
(respectively, a finite direct sum of chain rings) if and only if this mapping
λ : L(R) → L(RM) is a complete homomorphism for every simple (respectively,
cyclic) R-module M. A Noetherian ring R is an Artinian principal ideal
ring if and only if, for every R-module M, the mapping λ : L(R) → L(RM) is
a complete homomorphism.
Ayrıntılar
| Diğer ID | JA38YU69RD |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Aralık 2014 |
| Yayımlandığı Sayı | Yıl 2014 |