- In
abstract algebra, a
bimodule is an
abelian group that is both a left and a
right module, such that the left and
right multiplications are compatible...
- that are not. A
bimodule (or correspondence) is a
Hilbert space H with
module actions of two
commuting von
Neumann algebras.
Bimodules have a much richer...
-
condition can be
defined on
bimodule structures as well: an
Artinian bimodule is a
bimodule whose poset of sub-
bimodules satisfies the
descending chain...
- ) b . {\displaystyle D(ab)=aD(b)+D(a)b.} More generally, if M is an A-
bimodule, a K-linear map D : A → M that
satisfies the
Leibniz law is also called...
-
condition can also be
defined on
bimodule structures as well: a
Noetherian bimodule is a
bimodule whose poset of sub-
bimodules satisfies the
ascending chain...
-
defining a
maximal sub-
bimodule M of a
bimodule B to be a
proper sub-
bimodule of M
which is
contained in no
other proper sub-
bimodule of M. The
maximal ideals...
- (bs)} . If A is a (S,R)-
bimodule and B is a (R,T)-
bimodule, then A ⊗ R B {\displaystyle A\otimes _{R}B} is a (S,T)-
bimodule,
where the left and right...
- be
extended to
bimodules by
calling a non-zero sub-
bimodule N a
minimal sub-
bimodule of M if N
contains no
other non-zero sub-
bimodules. If the module...
- {\mathcal {D}}=\mathrm {Mod} _{R}.} Fix an ( R , S ) {\displaystyle (R,S)} -
bimodule X {\displaystyle X} and
define functors F : D → C {\displaystyle F\colon...
-
modules is
defined in a
similar way. One can also
define the
category of
bimodules over a ring R but that
category is
equivalent to the
category of left...
