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15
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Proof of Version of Krasner's Lemma

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#general-topology #ring-theory #commutative-algebra #algebraic-number-theory #galois-theory
78
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Equalities in the categories of modules

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#linear-algebra #abstract-algebra #ring-theory #category-theory #modules
1.2k
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Proving Fermat's Little Theorem and Euler's Generalization by Group Theory

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#abstract-algebra #group-theory #elementary-number-theory #ring-theory #modular-arithmetic
88
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Confusion about the definition of localization

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#abstract-algebra #ring-theory #commutative-algebra #localization
494
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A non-projective module

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#abstract-algebra #ring-theory #modules #noncommutative-algebra #projective-module
919
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Intersection of localizations of an integral domain

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#abstract-algebra #ring-theory #ideals #localization
2.3k
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Let R be an integral domain. Show that if the only ideals in R are {0} and R itself, R must be a field

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#abstract-algebra #ring-theory
346
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Module and Noetherian/Artinian Rings

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#abstract-algebra #ring-theory #field-theory #modules #noetherian
185
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Minimal Polynomial

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#abstract-algebra #polynomials #ring-theory #minimal-polynomials
362
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Criteria to check for subfield and subdomain

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#abstract-algebra #ring-theory #field-theory
138
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When to use Fermat's Little Theorem and Euler's Generalization of Fermat's Little Theorem

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#abstract-algebra #ring-theory
8.8k
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Commutative artinian ring is noetherian

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#abstract-algebra #ring-theory #commutative-algebra #alternative-proof #noetherian
250
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Can $\mathbb{Z}_{6}$ be a subring of some field?

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#abstract-algebra #ring-theory #proof-verification #field-theory
247
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Prove that some local noetherian integral domain is a field

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#abstract-algebra #ring-theory #commutative-algebra
799
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Zero divisors in the quotient $\mathbb{Z}[x]/(x^{2}+x-1)$

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#abstract-algebra #ring-theory

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