support (graded ring)

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

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

Title	support (graded ring)
Canonical name	SupportgradedRing
Date of creation	2013-03-22 15:40:00
Last modified on	2013-03-22 15:40:00
Owner	aplant (12431)
Last modified by	aplant (12431)
Numerical id	6
Author	aplant (12431)
Entry type	Definition
Classification	msc 13A02
Related topic	GradedRing
Defines	support
Defines	finite support