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- Irreducible_ring abstract "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."Meet-irreducible" rings are referred to as "irreducible rings" in commutative algebra. This article adopts the term "meet-irreducible" in order to distinguish between the several types being discussed.Meet-irreducible rings play an important part in commutative algebra, and directly irreducibe and subdirectly irreducible rings play a role in the general theory of structure for rings. Subdirectly irreducible algebras have also found use in number theory.This article follows the convention that rings have multiplicative identity, but are not necessarily commutative.".
- Irreducible_ring wikiPageID "23169189".
- Irreducible_ring wikiPageRevisionID "593673770".
- Irreducible_ring hasPhotoCollection Irreducible_ring.
- Irreducible_ring subject Category:Commutative_algebra.
- Irreducible_ring subject Category:Ring_theory.
- Irreducible_ring comment "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."Meet-irreducible" rings are referred to as "irreducible rings" in commutative algebra.".
- Irreducible_ring label "Irreducible ring".
- Irreducible_ring sameAs m.09gm2g6.
- Irreducible_ring sameAs Q6073577.
- Irreducible_ring sameAs Q6073577.
- Irreducible_ring wasDerivedFrom Irreducible_ring?oldid=593673770.
- Irreducible_ring isPrimaryTopicOf Irreducible_ring.