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Is $R$ a PID if every submodule of a free $R$-module is free?

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#abstract-algebra #ring-theory #commutative-algebra #modules
96
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How is this method of finding a maximal ideal specific to finite algebras over a field?

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#algebraic-geometry #commutative-algebra
335
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Integral extension and field

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#abstract-algebra #polynomials #commutative-algebra #integral-dependence
92
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Is quotient under $S_4$ action on "cube" representation a flat morphism?

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#abstract-algebra #algebraic-geometry #commutative-algebra #representation-theory
62
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When is a holomorphy ring a PID?

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#algebraic-geometry #commutative-algebra #algebraic-curves #principal-ideal-domains #function-fields
9.3k
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Prove every prime ideal of a ring is a radical ideal.

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#abstract-algebra #ring-theory #commutative-algebra #ideals
385
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Dimension of irreducible variety

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#algebraic-geometry #commutative-algebra
144
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A question about varieties (proposition from Miles Reid undergraduate comm algebra)

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#algebraic-geometry #commutative-algebra
444
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closed and open subscheme of affine scheme

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#algebraic-geometry #commutative-algebra
99
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Presentation of a local complete intersection

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#commutative-algebra
367
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Krull dimension and zero divisors of $k[x,y,z]/(x^ay,x^bz)$

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#commutative-algebra
394
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About images of (prime) ideals under injective endomorphisms

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#abstract-algebra #algebraic-geometry #commutative-algebra #ideals
157
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Is a vector of coprime ring elements column of an invertible matrix?

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#matrices #commutative-algebra #modules
448
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Example of Gorenstein local ring of dimension 1

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#commutative-algebra #gorenstein
4.6k
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Global sections of the projective space

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#algebraic-geometry #commutative-algebra

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