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About: Irreducible ring     Goto   Sponge   NotDistinct   Permalink

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In mathematics, especially in the field of ring theory, the term irreducible ring is used in a few different ways. * A (meet-)irreducible ring is one in which the intersection of two nonzero ideals is always nonzero. * A directly irreducible ring is ring which cannot be written as the direct sum of two nonzero rings. * A subdirectly irreducible ring is a ring with a unique, nonzero minimum two-sided ideal. This article follows the convention that rings have multiplicative identity, but are not necessarily commutative.