: of additive groups, such that
: for all nonnegative integers and .

A nonzero element of is said to be homogeneous of degree . By definition of a direct sum, every nonzero element of can be uniquely written as a sum where each is either 0 or homogeneous of degree . The nonzero are the homogeneous components of .

Some basic properties are:
* is a subring of ; in particular, the multiplicative identity is a homogeneous element of

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