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Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.

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#algebraic-geometry #ring-theory #commutative-algebra #nilpotence
57
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Extending a linear action to monomials of higher degree

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#linear-algebra #abstract-algebra #matrices #commutative-algebra #graded-rings
1.9k
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Tensor product commutes with infinite products

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#abstract-algebra #number-theory #commutative-algebra #algebraic-number-theory #tensor-products
1.2k
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Example of simple modules

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#abstract-algebra #commutative-algebra #modules #localization
105
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Describe explicitly a minimal free resolution

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#commutative-algebra #homological-algebra #formal-power-series
67
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Ideals of $k[[x,y]]$

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#commutative-algebra #ideals #formal-power-series
78
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$k[[x,y]]/I$ is a Gorenstein ring implies that $I$ is generated by 2 elements

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#commutative-algebra #gorenstein #regular-rings
174
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There is no ring map $\mathbb C[x] \to \mathbb C[x]$ swapping the prime ideals $(x-1)$ and $(x)$

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#abstract-algebra #algebraic-geometry #commutative-algebra
815
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Inclusions in tensor products

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#abstract-algebra #number-theory #commutative-algebra #algebraic-number-theory #tensor-products
404
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Principal Ideal Ring which is not Integral

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#abstract-algebra #commutative-algebra #principal-ideal-domains
185
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Hilbert polynomial and dimension of $M \otimes K(x_1,\dots,x_n)$

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#commutative-algebra #localization #hilbert-polynomial
1.1k
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Proving that the fraction field of a $k[x,y]/(f)$ is isomorphic to $k(t)$

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#abstract-algebra #commutative-algebra #field-theory
499
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projective module which is a submodule of a finitely generated free module

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#commutative-algebra #modules #projective-module #finitely-generated #free-modules
62
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Question about proof of Hilbert's Nullstellensatz

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#commutative-algebra #proof-explanation
84
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Exercise 15.10 in Cox's Book (first part)

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#abstract-algebra #number-theory #commutative-algebra #modules #algebraic-number-theory

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