# support (graded ring)

Let $S$ be a groupoid (semigroup, group) and suppose $R=\bigoplus_{s\in S}R_{s}$ is an $S$- graded ring.

We define the of $r$ to be the set $\,{\rm supp}\,(r)=\{s\in S\mid r_{s}\neq 0\}$. We can extend this definition to $\,{\rm supp}\,(R)=\bigcup\,{\rm supp}\,R_{s}\neq 0\}$. If $\,{\rm supp}\,(R)$ is a finite set then we say that the ring $R$ has finite support.

Title support (graded ring) SupportgradedRing 2013-03-22 15:40:00 2013-03-22 15:40:00 aplant (12431) aplant (12431) 6 aplant (12431) Definition msc 13A02 GradedRing support finite support