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15
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Is my understanding about a lemma regarding ring of polynomials correct?

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#abstract-algebra #polynomials #ring-theory
195
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Sum and Intersection of Contraction and Extension

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#abstract-algebra #ring-theory #ideals
233
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Stalks, Germs and Localisation

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#algebraic-geometry #ring-theory #sheaf-theory #affine-varieties #germs
17
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Some confusion about coordinate and quotient rings

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#ring-theory
113
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What is the difference between $K[X_1, \ldots, X_{m - 1}]\color{blue}{[X]}$ and $K[X_1, \ldots, X_{m - 1}]\color{blue}{[X_{m}]}$?

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#abstract-algebra #polynomials #ring-theory #definition #formal-power-series
32
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Understanding a specific quotient ring

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#polynomials #ring-theory #quotient-spaces
232
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Invertible elements in a discrete valuation ring

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#abstract-algebra #ring-theory #inverse #valuation-theory #local-rings
126
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Expressing an ideal as intersection of prime ideals

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#ring-theory
39
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Let $I\subseteq R$ be an ideal of a ring $R$. For any $a\in R$, $l_{R/I}(a+I)=l_{R/I}(a)$

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#ring-theory
141
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show a quotient ring is a field

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#abstract-algebra #ring-theory #field-theory
58
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Closed subset $Z \subseteq \operatorname{Spec} A$

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#abstract-algebra #algebraic-geometry #ring-theory #commutative-algebra
428
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is the ideal $(x-y,x+y)$ same as $(x,y)$

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#ring-theory #ideals
796
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is $(x+y,x-y)$ a prime ideal in $\mathbb{Z}[X,Y] $

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#abstract-algebra #ring-theory
103
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Hereditary torsion theories and preradicals

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#ring-theory #modules
133
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How to prove that a ring ideal is not principal?

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#abstract-algebra #ring-theory #ideals

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