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irreducible (Definition)

Let $ r$ be a non-unit of an integral domain $ D$. We say that $ r$ is irreducible in $ D$, if any factorization $ r = ab$ in $ D$ requires that $ a$ or $ b$ is a unit.



"irreducible" is owned by drini. [ full author list (2) | owner history (1) ]
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See Also: UFD, divisibility in rings, PID, irreducible polynomial

Also defines:  irreducible element

Attachments:
ring without irreducibles (Example) by pahio
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Cross-references: unit, integral domain
There are 36 references to this entry.

This is version 3 of irreducible, born on 2001-11-04, modified 2005-05-01.
Object id is 668, canonical name is Irreducible.
Accessed 5316 times total.

Classification:
AMS MSC: 13G05 (Commutative rings and algebras :: Integral domains)
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