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Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain.

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#abstract-algebra #ring-theory #integral-domain #polynomial-rings
78
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GCD of common divisors in integral domain

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#abstract-algebra #gcd-and-lcm #integral-domain
1k
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Jacobson radical of formal power series over an integral domain

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#abstract-algebra #ring-theory #integral-domain #formal-power-series
310
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Characteristic of an integral domain: doubt in the proof

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#ring-theory #integral-domain #positive-characteristic
147
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When prime element in an integral domain stays prime in integral extension

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#ring-theory #commutative-algebra #integral-domain #integral-extensions
523
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Localization in integral domains

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#maximal-and-prime-ideals #localization #integral-domain
755
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Module over integral domain, "Rank-nullity theorem", Exact Sequence

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#abstract-algebra #modules #exact-sequence #integral-domain #finitely-generated
173
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Why must a domain be nonzero?

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#abstract-algebra #ring-theory #definition #integral-domain
130
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Contraction of primes associated to nonzerodivisors

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#abstract-algebra #ring-theory #commutative-algebra #integral-domain
339
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Abstract algebra for $\mathbb Z_p[i]$ form a field

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#abstract-algebra #integral-domain
173
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Associated primes to principal ideals in a Noetherian domain

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#ring-theory #commutative-algebra #localization #noetherian #integral-domain
40
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Closure of a characteristic in an integral domain

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#ring-theory #integral-domain
7.6k
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Prove that $\mathbb{Z}[i]$ is an integral domain.

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#proof-verification #ring-theory #integral-domain #gaussian-integers
60
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The ideals of $\mathbb{Z}_{(p)}$ = {$m/n \in \mathbb{Q} : p$ does not divide $n$}.

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#abstract-algebra #ring-theory #ideals #principal-ideal-domains #integral-domain
1.5k
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An $n$ degree polynomial with more than $n$ roots?

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#abstract-algebra #polynomials #roots #integral-domain

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