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15
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Resultants of two polynomials over a ring

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#abstract-algebra #algebraic-geometry #commutative-algebra
452
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Exercise on localization as a colimit

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#abstract-algebra #commutative-algebra
61
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Example of commutative algebra over integers where there exists $x$ such that $x = y^2$ for several $y$'s

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#abstract-algebra #ring-theory #commutative-algebra
282
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Modules with finite support in $\mathrm{Max}(R)$

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#abstract-algebra #commutative-algebra #modules
105
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The injectivity of $f\mapsto f\circ v$ on $\hom(M'',N)$ implies that $v$ is surjective

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#commutative-algebra #homological-algebra
563
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For a discrete valuation ring to be a PID, must it have an element of valuation 1?

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#abstract-algebra #commutative-algebra
290
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Example of a module such that every proper submodule is finitely generated but the module is not.

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#ring-theory #commutative-algebra #modules
117
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Condition on a field that makes every subring an integrally closed domain

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#abstract-algebra #ring-theory #commutative-algebra
185
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Functorial approach to Ideals and Quotients, Multiplicative Sets and Localizations

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#ring-theory #commutative-algebra #category-theory #ideals #universal-algebra
350
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An ideal that contained in finitely many maximal ideals but all of its elements contained in infinitely many maximal ideals

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#commutative-algebra
423
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Valuation rings of $k(X)$

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#abstract-algebra #ring-theory #commutative-algebra
874
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Why is $W_n(k)$ the unique flat lifting of a perfect field $k$ over $\mathbf{Z}/p^n$?

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#algebraic-geometry #commutative-algebra #positive-characteristic
80
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Calculating the kernel of a homomorphism

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#ring-theory #commutative-algebra
567
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Bruns-Herzog, Cohen-Macaulay Rings, Exercise 6.4.17 (b)

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#commutative-algebra #maximal-and-prime-ideals #cohen-macaulay
500
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Ideal generated by a regular sequence

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#algebraic-geometry #ring-theory #commutative-algebra #ideals

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