Noetherian ring
Noetherian ring In abstract algebra, a Noetherian ring is a ring that satisfies the ascending chain condition ...
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Talk:Noetherian ring
Talk:Noetherian ring The article states that noetherian implies every ideal is finitely generated; shouldn ... finitely generated, since for example, Q is noetherian (every field is), and yet Q cannot ...
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Noetherian
Noetherian In mathematics, Noetherian is an adjective derived from the name ... condition on certain kinds of subobjects. A Noetherian ring is a ring that satisfies the ascending chain condition ...
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Local ring
Local ring In mathematics, more particularly in abstract algebra ... in 1938. Definition and first consequences A ring R is a local ring if it has one (and therefore all ... unique maximal right ideal and with the ring's Jacobson radical. The third of the ... set of non-units in a local ring forms a (proper) ideal, necessarily contained ...
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Noetherian module
Noetherian module In ring theory, if R is a ring and M is a module over R, then M is Noetherian if M satisfies the ascending chain condition ... submodules when they are ordered by inclusion. Noetherian modules are named in honor of ...
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Polynomial ring
Polynomial ring In abstract algebra, a polynomial ring is the set of polynomials in one ... or more variables with coefficients in a ring. Definition of a polynomial In real analysis ... definition cannot be adapted to a general ring, however. For example, over the ring Z/2Z of integers modulo 2, ...
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Gorenstein ring
Gorenstein ring In commutative algebra, a Gorenstein local ring is a Noetherian commutative local ring R with finite injective dimension, as an ... sort of duality condition. A Gorenstein commutative ring is a commutative ring such that ...
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Artinian ring
Artinian ring In abstract algebra, an Artinian ring is a ring that satisfies the descending chain condition on ... to distinguish three very similar concepts: A ring is left Artinian if it satisfies the ... descending chain condition on left ideals. A ring is right Artinian if it satisfies ...
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Glossary of ring theory
Glossary of ring theory Ring theory is the branch of mathematics in ... terms of the subject. Definition of a ring Ring A ring is a set R with two ...
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Talk:Local ring
Talk:Local ring About the noetherian condition - can I explain that Zariski in particular took local ring to be noetherian? This is however not the modern convention ... practice followed, for example, in defining a ring (mathematics) always to be unital here. ...
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