1. This is up to isomorphism the only indecomposable module over " R ". 2. The indecomposable modules in wild blocks are extremely difficult to classify, even in principle. 3. Principal indecomposable modules are also called "'PIM "'s for short. 4. In ordinary representation theory, every indecomposable module is irreducible, and so every module is projective. 5. In all other cases, there are infinitely many isomorphism types of indecomposable modules in the block. 6. One had the remarkable extensions of Clifford theory by Green to the indecomposable modules of group algebras. 7. In particular, A should have two irreducible modules and six indecomposable modules , all of which are submodules of A. 8. An indecomposable module is a non-zero module that cannot be written as a direct sum of two non-zero submodules. 9. Every simple module is indecomposable, but there are indecomposable modules which are not simple ( e . g . uniform modules ). 10. When q _ i = 0, the resulting indecomposable module is R itself, and this is inside the part of " M " that is a free module.
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