PlanetMath: completely reducible

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completely reducible

(Definition)

A module is called completely reducible (or semisimple) if it is a direct sum of irreducible (or simple) modules.

"completely reducible" is owned by Mathprof. [ full author list (2) | owner history (1) ]

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Other names:

semisimple

Also defines:

semisimple

Attachments:: example of reducible and irreducible -modules (Example) by rm50

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Cross-references: simple, irreducible, direct sum, module
There are 11 references to this entry.

This is version 4 of completely reducible, born on 2003-01-04, modified 2007-01-27.
Object id is 3873, canonical name is CompletelyReducible.
Accessed 4575 times total.

Classification:

16D60 (Associative rings and algebras :: Modules, bimodules and ideals :: Simple and semisimple modules, primitive rings and ideals)

Pending Errata and Addenda

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