PlanetMath: simple ring

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simple ring

(Definition)

A nonzero ring $R$ is said to be a simple ring if it has no (two-sided) ideal other then the zero ideal and $R$ itself.

This is equivalent to saying that the zero ideal is a maximal ideal.

If $R$ is a commutative ring with unit, then this is equivalent to being a field.

"simple ring" is owned by antizeus.

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Cross-references: field, unit, commutative ring, maximal ideal, equivalent, zero ideal, ideal, ring
There are 8 references to this entry.

This is version 4 of simple ring, born on 2001-10-20, modified 2002-10-25.
Object id is 414, canonical name is SimpleRing.
Accessed 3908 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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