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quotient ring of the class $C^{\infty}$ functions on $\mathbb{R}$

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#abstract-algebra #ring-theory #maximal-and-prime-ideals #formal-power-series
247
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Finding Galois group of function field extension

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#galois-theory #extension-field #laurent-series #splitting-field #formal-power-series
95
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Puiseux series over positve charactersitc field

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#field-theory #laurent-series #formal-power-series
1k
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The field of fractions of $\mathbb{Z}[[X]]$ and $\mathbb{Q}[[X]]$, the power series rings, are different.

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#abstract-algebra #ring-theory #field-theory #formal-power-series
52
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"Symbolic" relation between moments and cumulants

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#sequences-and-series #statistics #moment-generating-functions #formal-power-series #cumulants
320
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Computing ideal of initial forms

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#polynomials #commutative-algebra #ideals #graded-rings #formal-power-series
497
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Explanation of a proof from Stacks Project: Noetherian ring of formal powers series

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#abstract-algebra #proof-verification #commutative-algebra #proof-explanation #formal-power-series
139
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Compositional inverse series of a convergent power series

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#sequences-and-series #complex-analysis #convergence-divergence #power-series #formal-power-series
99
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Why some authors take $A[[t]]$ as $A \otimes_k k[[t]]$ when defining formal deformations?

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#formal-power-series #deformation-theory
81
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Is the solution to the functional equation $\widehat{F}(z) = z\widehat{G}(\widehat{F}(z))$ unique?

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#combinatorics #generating-functions #trees #formal-power-series #lagrange-inversion
47
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$f(x)= \frac{1}{x^{2}-3x-4} $The power series expansion at x = 1.

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#power-series #formal-power-series #perfect-powers
572
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Matsumura, Exercise 18.8: Cohen-Macaulay and (not) Gorenstein

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#ring-theory #commutative-algebra #formal-power-series #cohen-macaulay #gorenstein
101
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Can $R[[x]]$ contain constants?

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#abstract-algebra #commutative-algebra #formal-power-series
785
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Power series solution to integral equation

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#definite-integrals #power-series #integral-equations #formal-power-series
145
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Short form of few series

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#sequences-and-series #power-series #fourier-series #divergent-series #formal-power-series

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