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15
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Roots over the complex numbers

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#abstract-algebra #roots #unique-factorization-domains
89
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A variation on $6=2 \cdot 3=(1+\sqrt {-5})(1-\sqrt {-5})$

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#commutative-algebra #integral-domain #unique-factorization-domains
621
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How to show a polynomial over a UFD, which is reducible over field of fractions, can be factored over the ring?

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#abstract-algebra #polynomials #ring-theory #factoring #unique-factorization-domains
78
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Relation between two problems of algebraic number theory

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#number-theory #algebraic-number-theory #unique-factorization-domains
87
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Mutual indivisibility and ideals

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#abstract-algebra #ring-theory #unique-factorization-domains
88
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Showing irreducibility is invariant under conjugation in quadratic integers

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#number-theory #extension-field #prime-factorization #unique-factorization-domains
140
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Number of irreducible divisors in a UFD

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#abstract-algebra #ring-theory #prime-factorization #unique-factorization-domains
717
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Is $\mathcal{O}_{\mathbb{Q}(\sqrt{5})}$ is a UFD

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#abstract-algebra #ring-theory #unique-factorization-domains
83
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Flatness of $\frac{R[T]}{I}$ over $R$ implies that $I$ is principal or $I=R[T]$?

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#commutative-algebra #unique-factorization-domains #flatness
66
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On the unique factorisation of $R[x_1,y_1,...,x_n,y_n]/(x_1y_1+...+x_ny_n)$ where $R$ is UFD

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#commutative-algebra #unique-factorization-domains
118
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Factorization in a principal ideal ring/rng

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#abstract-algebra #prime-factorization #principal-ideal-domains #unique-factorization-domains #rngs
60
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When $d \in D$ irreducible implies $d+I \in \frac{D}{I}$ irreducible?

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#algebraic-geometry #commutative-algebra #irreducible-polynomials #unique-factorization-domains
129
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Concerning $g=qf+r$, where $f,g \in k[x,y]$

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#polynomials #euclidean-algorithm #unique-factorization-domains
81
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Application of Noether-Lefschetz theorem

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#algebraic-geometry #polynomials #commutative-algebra #unique-factorization-domains
168
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When every prime/irreducible element remains prime/irreducible in a ring extension

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#algebraic-geometry #commutative-algebra #irreducible-polynomials #integral-domain #unique-factorization-domains

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