-
condition on
submodules, that is,
every increasing chain of
submodules becomes stationary after finitely many steps. Equivalently,
every submodule is finitely...
- 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...
- may
alternatively be said that "N ⊆ M is a
rational extension".
Dense submodules are
connected with
rings of
quotients in
noncommutative ring theory. Most...
-
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...
-
acting on V are
cyclic submodules. (The
Jordan blocks are all
isomorphic to F[x] / (x − λ)n;
there may also be
other cyclic submodules with
different annihilators;...
-
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...
- of
modules is the
smallest module which contains the
given modules as
submodules with no "unnecessary" constraints,
making it an
example of a coproduct...
-
finitely generated module admits maximal submodules. If any
increasing chain of
submodules stabilizes (i.e., any
submodule is
finitely generated), then the module...
- {Z}}(_{R}R)} . Here are
several definitions used when
studying singular submodules and
singular ideals. In the following, M is an R-module: M is
called a...
-
series for
modules restricts all
attention to
submodules,
ignoring all
additive subgroups that are not
submodules.
Given a ring R and an R-module M, a composition...
