13A02-SupportgradedRing.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{SupportgradedRing}
\pmcreated{2013-03-22 15:40:00}
\pmmodified{2013-03-22 15:40:00}
\pmowner{aplant}{12431}
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\pmtitle{support (graded ring)}
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\pmauthor{aplant}{12431}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{13A02}
%\pmkeywords{support}
%\pmkeywords{finite support}
\pmrelated{GradedRing}
\pmdefines{support}
\pmdefines{finite support}

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

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