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[parent] support (graded ring) (Definition)

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

We define the support 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.



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See Also: graded ring

Also defines:  support, finite support
Keywords:  support, finite support

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Cross-references: ring, finite set, graded ring, group, semigroup, groupoid
There are 17 references to this entry.

This is version 3 of support (graded ring), born on 2006-02-06, modified 2006-02-06.
Object id is 7601, canonical name is SupportGradedRing.
Accessed 2275 times total.

Classification:
AMS MSC: 13A02 (Commutative rings and algebras :: General commutative ring theory :: Graded rings)
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