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support (Definition)

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

The maximal support $\Supp_m(M)$ of a module $M$ over a ring $R$ is the set of all maximal ideals $\m \subset R$ such that $M_\m$ is nonzero.




"support" is owned by djao.
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Cross-references: maximal ideals, localization, prime ideals, ring, module
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This is version 2 of support, born on 2002-01-06, modified 2002-01-26.
Object id is 1406, canonical name is Support.
Accessed 4545 times total.

Classification:
AMS MSC13C99 (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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