indecomposable การใช้

• Alternatively, it is an indecomposable, projective, cyclic module.
• Let " A " be an indecomposable generalized Cartan matrix.
• Uniserial modules are uniform, and uniform modules are necessarily directly indecomposable.
• Here, uniqueness means direct decompositions into indecomposable subgroups have the exchange property.
• Symmetrizable indecomposable generalized Cartan matrices of finite and affine type have been completely classified.
• Otherwise, it is said to be indecomposable.
• This is up to isomorphism the only indecomposable module over " R ".
• The indecomposable modules in wild blocks are extremely difficult to classify, even in principle.
• Strictly speaking, the multiplicatively indecomposable ordinal.
• Obviously 1 is additively indecomposable, since 0 + 0 No cardinal is additively indecomposable.
• Obviously 1 is additively indecomposable, since 0 + 0 No cardinal is additively indecomposable.
• Principal indecomposable modules are also called "'PIM "'s for short.
• In this way there is a 1-1 correspondence between prime ideals and indecomposable injective modules.
• In ordinary representation theory, every indecomposable module is irreducible, and so every module is projective.
• In all other cases, there are infinitely many isomorphism types of indecomposable modules in the block.
• One had the remarkable extensions of Clifford theory by Green to the indecomposable modules of group algebras.
• Every finitely-generated abelian group is a direct sum of ( finitely many ) indecomposable abelian groups.
• A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group.
• Over a Noetherian ring, every injective module is the direct sum of ( uniquely determined ) indecomposable injective modules.
• In particular, A should have two irreducible modules and six indecomposable modules, all of which are submodules of A.