-
condition on
submodules, that is,
every increasing chain of
submodules becomes stationary after finitely many steps. Equivalently,
every submodule is finitely...
-
lattice isomorphism between the
lattice of
submodules of M / N {\displaystyle M/N} and the
lattice of
submodules of M {\displaystyle M} that
contain N {\displaystyle...
-
submodules. However, as
noted above,
finitely generated nonzero modules have
maximal submodules, and also
projective modules have
maximal submodules....
-
module that
satisfies the
ascending chain condition on its
submodules,
where the
submodules are
partially ordered by inclusion. Historically,
Hilbert was...
- the
minimal submodules are
exactly the
minimal right ideals of R. Likewise, the
minimal left
ideals of R are
precisely the
minimal submodules of the left...
- pure
exact if and only if C is flat. From this one can
deduce that pure
submodules of flat
modules are flat.
Suppose C is flat. Then B is flat if and only...
-
submodules, but not everything.
Again let M be a module, and K, N and H be
submodules of M with K ⊆ {\displaystyle \subseteq } N. The zero
submodule is...
- ring. The
torsion submodule of a
module is the
submodule formed by the
torsion elements (in
cases when this is
indeed a
submodule, such as when the ring...
-
stating that
every submodule of a
finitely generated module over a
Noetherian ring is a
finite intersection of
primary submodules. This
contains the case...
- may
alternatively be said that "N ⊆ M is a
rational extension".
Dense submodules are
connected with
rings of
quotients in
noncommutative ring theory. Most...
