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15
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Characterize ideals in polynomial ring in terms of ideals in the coefficient ring.

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#polynomials #ring-theory #commutative-algebra #ideals #noetherian
87
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The set of non-zero-divisors is dense in the $\mathfrak m$-adic topology for a Noetherian local ring of positive depth

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#abstract-algebra #commutative-algebra #noetherian #local-rings
63
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The intersection of all curves is the intersection of a finite number of curves

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#ring-theory #commutative-algebra #algebraic-curves #noetherian #polynomial-rings
59
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the intersection of all curves is not empty.

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#ring-theory #commutative-algebra #algebraic-curves #noetherian #polynomial-rings
72
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Finitely generated $M$ at each prime

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#commutative-algebra #noetherian
54
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Proving that this kind of matrix ring is left Noetherian but not right Noetherian

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#abstract-algebra #ring-theory #modules #extension-field #noetherian
521
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If $R$ is a Noetherian ring, then $R^n$ is Noetherian

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#abstract-algebra #ring-theory #modules #noetherian #finitely-generated
78
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If $A$ is Noetherian ring with ideal $I$, then $I$-adic completion ${\hat{A}}$ is Noetherian

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#algebraic-geometry #commutative-algebra #cauchy-sequences #noetherian #artinian
54
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Irredundant primary decomposition of radical from irredundant primary decomposition under certain conditions

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#abstract-algebra #commutative-algebra #noetherian #primary-decomposition
72
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Noetherian rings and greatest common divisors of ideals.

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#abstract-algebra #ring-theory #gcd-and-lcm #noetherian
113
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Ideal of definition of local ring

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#algebraic-geometry #commutative-algebra #noetherian #local-rings #artinian
61
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Annihilators of elements in the associated graded ring

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#commutative-algebra #noetherian
145
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What is this ring $\mathbb{Z}[x,1/x]$?

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#abstract-algebra #group-theory #ring-theory #noetherian
33
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Hint about a problem with Noethenian rings and its ellements

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#ring-theory #noetherian
50
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A Noetherian-as-a-module ring is Noetherian as a ring?

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#abstract-algebra #ring-theory #modules #ideals #noetherian

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