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Factorizing polynomials in a field.

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#abstract-algebra #ring-theory #finite-fields #unique-factorization-domains
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$\mathbb Z[\sqrt{13}]$ is not a UFD.

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#abstract-algebra #unique-factorization-domains
118
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Proof that 7 is irreducible in $\mathbb Z[\sqrt{15}]$.

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#abstract-algebra #unique-factorization-domains
21
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A confusion about UFDs

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#unique-factorization-domains
699
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Is $\mathbb{Z}[√13] $ a Unique factorization domain?

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#abstract-algebra #ring-theory #irreducible-polynomials #prime-factorization #unique-factorization-domains
443
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$\mathbb{Z}[2\sqrt2]$ is not a UFD.

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#unique-factorization-domains #polynomial-rings
643
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Prove $x^2-\sqrt2$ is irreducible over $\mathbb{Z}[\sqrt 2]$

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#unique-factorization-domains #polynomial-rings
34
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Explanation for some parts of this proof.

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#ring-theory #gcd-and-lcm #unique-factorization-domains
367
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Prove general Euclid's Lemma in a UFD using prime factorization

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#ring-theory #proof-writing #unique-factorization-domains
52
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what does $x|1$ mean in a UFD?

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#abstract-algebra #divisibility #unique-factorization-domains
703
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The intersection of any family of principal ideals in a UFD is principal

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#abstract-algebra #solution-verification #gcd-and-lcm #unique-factorization-domains
53
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How is $\mathbb C(x)^*$ a free group?

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#polynomials #examples-counterexamples #free-groups #unique-factorization-domains #polynomial-rings
184
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Can you suggest some challenging ring theory problems?

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#ring-theory #principal-ideal-domains #unique-factorization-domains
80
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If $(a,b)=1$ and $a|c$ and $b|c$ then $ab|c$

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#abstract-algebra #unique-factorization-domains
104
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Using the Multidegree on a Polynomial Identity to Prove a Set Containment

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#ring-theory #unique-factorization-domains #polynomial-rings

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