-
condition on
submodules, that is,
every increasing chain of
submodules becomes stationary after finitely many steps. Equivalently,
every submodule is finitely...
-
submodules. However, as
noted above,
finitely generated nonzero modules have
maximal submodules, and also
projective modules have
maximal submodules....
-
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, 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...
- may
alternatively be said that "N ⊆ M is a
rational extension".
Dense submodules are
connected with
rings of
quotients in
noncommutative ring theory. Most...
-
module that
satisfies the
ascending chain condition on its
submodules,
where the
submodules are
partially ordered by inclusion. Historically,
Hilbert was...
- 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...
-
finitely generated module admits maximal submodules. If any
increasing chain of
submodules stabilizes (i.e., any
submodule is
finitely generated), then the module...
-
stating that
every submodule of a
finitely generated module over a
Noetherian ring is a
finite intersection of
primary submodules. This
contains the case...
- non-zero and have no non-zero
proper submodules. Equivalently, a
module M is
simple if and only if
every cyclic submodule generated by a non-zero
element of...
