support (graded ring) (original) (raw)

Let S be a groupoid (semigroup, group) and suppose R=⊕s∈SRs is an S- graded ring.

We define the support of r to be the set supp⁢(r)={s∈S∣rs≠0}. We can extend this definition to supp(R)=⋃suppRs≠0}. If supp⁢(R) is a finite set then we say that the ring R has finite support.