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Divided power algebra is artinian as a module over the polynomial ring

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#abstract-algebra #commutative-algebra #graded-modules #local-rings #artinian
420
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Integral extension of a local ring is semilocal

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#commutative-algebra #local-rings #cohen-macaulay
64
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Showing some element is a zero divisor

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#commutative-algebra #direct-product #local-rings
61
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Adjoining an element with given minimal polynomial to a DVR of characteristic p.

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#abstract-algebra #algebraic-number-theory #valuation-theory #local-rings
231
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Commutative local ring with $10$ ideals

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#ring-theory #commutative-algebra #ideals #local-rings #artinian
380
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When is a map of local rings finite?

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#algebraic-geometry #commutative-algebra #affine-schemes #local-rings
2.4k
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Quotient ring local if Ring is local

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#abstract-algebra #ring-theory #factoring #quotient-group #local-rings
51
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Existence of ideal in Cohen-Macaulay ring, going modulo which still gives Cohen-Macaulay

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#commutative-algebra #noetherian #krull-dimension #local-rings #cohen-macaulay
214
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Exercise 4.4.1 in Weibel's 'An Introduction to Homological Algebra'.

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#commutative-algebra #homological-algebra #local-rings #regular-rings
71
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Theorem on Injective Dimension in Weibel's "An Introduction to Homological Algebra"

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#commutative-algebra #homological-algebra #injective-module #local-rings
105
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Every finite integral extension of a Henselian, pseudo-geometric and analytically normal ring is algebraically closed in its completion.

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#algebraic-geometry #commutative-algebra #local-rings #hensels-lemma
412
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Is the ring $\mathbb{Z}_{p^n}$ local?

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#abstract-algebra #ring-theory #local-rings
701
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The residue field of valuations are finite extension

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#abstract-algebra #commutative-algebra #valuation-theory #local-rings
108
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Consequence of local duality

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#algebraic-geometry #commutative-algebra #local-rings
128
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Completion of the local ring at a point on arithmetic surfaces.

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#algebraic-geometry #power-series #surfaces #local-rings

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