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Let $R$ be a ring with unity. Can anybody please help me giving a definition of what the homogeneous component of an $R$-module $M$ is. I searched for the definition but I never got it.

I appreciate any help. Thanks in advance.

The citation below is taken out of a paper not a book.

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Hussein Eid
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    See the wikipedia page for graded modules. The idea is that if $M$ is graded as $M = \bigoplus M_i$, then each fixed $M_i$ is a homogeneous component of $M$. – HallaSurvivor Oct 25 '21 at 02:39
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    For a semisimple module it could also refer to the submodules which are sums of mutually isomorphic simple submodules. – rschwieb Oct 25 '21 at 03:36
  • I edited the post. The module is not necessarily semisimple. @rschwieb . Also, what is meant precisely by "complete sum". I'm actually familiar with "internal direct sum" and "external direct sums". – Hussein Eid Oct 25 '21 at 22:09

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