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Form of $(x,y) \mapsto (\lambda x^n+\cdots,\mu x^n+\cdots) \in k[x^{1/m},x^{-1/m},y]$

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#polynomials #ring-theory #commutative-algebra
263
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An integral domain $R$ with fraction field $K$ satisfying this property is a local ring?

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#abstract-algebra #ring-theory #commutative-algebra
648
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A variety $X$ is irreducible $\iff I(X)$ is prime

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#commutative-algebra #roots #maximal-and-prime-ideals #affine-varieties
51
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Computation of Rees algebra of polynomial ideal

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#algebraic-geometry #commutative-algebra
275
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Atiyah Macdonald exercise 1.5

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#commutative-algebra
61
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Codimension of Generic Fiber

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#algebraic-geometry #commutative-algebra #flatness
157
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Let $R$ be a ring. Prove $I \oplus J \cong R \oplus IJ$ as $R$-modules.

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#abstract-algebra #ring-theory #commutative-algebra #modules
149
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Dimension of Intersection of Algebraic Sets

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#algebraic-geometry #commutative-algebra #affine-varieties
46
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A question in $I$-adic rings

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#abstract-algebra #ring-theory #commutative-algebra
819
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All prime ideals of $R/I$ where $R$ is the infinite polynomial ring

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#abstract-algebra #ring-theory #commutative-algebra
127
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preimage of integral extension of ideal

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#ring-theory #commutative-algebra #ideals
183
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Prove that $g(x)=0$ for all $x$.

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#abstract-algebra #polynomials #ring-theory #commutative-algebra #integral-domain
85
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Faithful flatness of equalizers

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#commutative-algebra
209
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Tensor product of commutative rings of characteristic zero

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#commutative-algebra #tensor-products
45
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Proving that $S^{-1} A \cong \mathbb{R}[X, X^{-1}]$ (ring of fractions)

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#abstract-algebra #ring-theory #commutative-algebra

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