PlanetMath: support

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support

(Definition)

The support $\operatorname{Supp}(M)$ of a module over a ring is the set of all prime ideals ${\mathfrak{p}}\subset R$ such that the localization $M_{\mathfrak{p}}$ is nonzero.

The maximal support $\operatorname{Supp}_m(M)$ of a module over a ring is the set of all maximal ideals ${\mathfrak{m}}\subset R$ such that $M_{\mathfrak{m}}$ is nonzero.

"support" is owned by djao.

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Cross-references: maximal ideals, localization, prime ideals, ring, module
There are 31 references to this entry.

This is version 2 of support, born on 2002-01-06, modified 2002-01-26.
Object id is 1406, canonical name is Support.
Accessed 3289 times total.

Classification:

AMS MSC:	13C99 (Commutative rings and algebras :: Theory of modules and ideals :: Miscellaneous)
	16D10 (Associative rings and algebras :: Modules, bimodules and ideals :: General module theory)

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