Modules over a Dedekind domain #
Over a Dedekind domain, an I
-torsion module is the internal direct sum of its p i ^ e i
-torsion
submodules, where I = ∏ i, p i ^ e i
is its unique decomposition in prime ideals.
Therefore, as any finitely generated torsion module is I
-torsion for some I
, it is an internal
direct sum of its p i ^ e i
-torsion submodules for some prime ideals p i
and numbers e i
.
Over a Dedekind domain, an I
-torsion module is the internal direct sum of its p i ^ e i
-
torsion submodules, where I = ∏ i, p i ^ e i
is its unique decomposition in prime ideals.
A finitely generated torsion module over a Dedekind domain is an internal direct sum of its
p i ^ e i
-torsion submodules where p i
are factors of (⊤ : Submodule R M).annihilator
and
e i
are their multiplicities.
A finitely generated torsion module over a Dedekind domain is an internal direct sum of its
p i ^ e i
-torsion submodules for some prime ideals p i
and numbers e i
.