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Monthly Archives: March 2015
Modular Representation Theory (IV)
Continuing our discussion of modular representation theory, we will now discuss block theory. Previously, we saw that in any ring R, there is at most one way to write where is a set of orthogonal and centrally primitive idempotents. If such an … Continue reading
Idempotents and Decomposition
Let R be a general ring, not necessarily commutative. An element x∈R is said to be idempotent if x2 = x. Note An endomorphism f of an Rmodule M (i.e. ) is an idempotent if and only if f is a projection, i.e. M = ker(f) ⊕ im(f) and f … Continue reading
Posted in Notes
Tagged blocks, idempotents, indecomposable modules, modules, primitive idempotents
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