Explore: Indecomposable Modules

indecomposable modules can then be thought of as the "basic building blocks", the only objects that need to be studied. This is the case for modules over

every injective module is uniquely a direct sum of indecomposable modules, and their structure is well understood. An injective module over one ring may

simple module is indecomposable, but there are indecomposable modules that are not simple (e.g. uniform modules). Faithful A faithful module M is one

multiplicities of the respective simple modules as composition factors of the j-th projective indecomposable module. The Cartan matrix is non-singular; in

as module theory, a principal indecomposable module has many important relations to the study of a ring's modules, especially its simple modules, projective

R/(q_{i})} are indecomposable, so the primary decomposition is a decomposition into indecomposable modules, and thus every finitely generated module over a PID

mathematics: Indecomposable module, in algebra Indecomposable distribution, in probability Indecomposable continuum, in topology Indecomposability (intuitionistic

states that if a module has an decomposition into modules with local endomorphism rings, then all decompositions into indecomposable modules are equivalent

over Z, this is a complete list of indecomposable algebraically compact modules. Many algebraically compact modules can be produced using the injective

The simple modules are precisely the modules of length 1; this is a reformulation of the definition. Every simple module is indecomposable, but the converse