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Greatest common divisor on a factorial domain proof (Integers)

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#ring-theory #proof-writing #unique-factorization-domains
143
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Is C[X,Y]/<XY> isomorphic to the product ring (C[X]/<X>)×(C[Y]/<Y>)

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#abstract-algebra #polynomials #ring-theory #ideals #unique-factorization-domains
114
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Why is $\mathbb{Z}[i \sqrt{2}]$ a Unique Factorization Domain

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#abstract-algebra #unique-factorization-domains
117
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What kind of subrings inherit their parent ring's properties?

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#abstract-algebra #ring-theory #principal-ideal-domains #integral-domain #unique-factorization-domains
113
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Define an isomorphism between finite boolean ring and $\mathbb{Z}_2\times \cdots\times \mathbb{Z}_2$

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#abstract-algebra #ring-theory #unique-factorization-domains #ring-isomorphism #boolean-ring
90
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Is $ \mathbb{Z}^+ [ x ] \backslash \{ 0 \} $ a unique factorization monoid with respect to the usual product?

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#monoid #unique-factorization-domains
45
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How can we extend the notion of unique factorization monoid to arbitrary products?

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#infinite-product #monoid #unique-factorization-domains
92
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Properties of $\mathbb{C}+(h) \subseteq \mathbb{C}[x]$

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#algebraic-geometry #ring-theory #commutative-algebra #unique-factorization-domains #flatness
355
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Is there an integral domain containing an element having no factorization into irreducible elements?

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#ring-theory #commutative-algebra #unique-factorization-domains
69
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Is the ring $\frac{\Bbb{C}[X,Y,Z]}{(XY-Z)}$ a UFD?

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#abstract-algebra #unique-factorization-domains
136
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UFD with no efficient GCD algorithm

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#abstract-algebra #computational-complexity #unique-factorization-domains #computational-number-theory
110
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On isomorphism of two quotient of polynomial rings

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#abstract-algebra #ring-theory #irreducible-polynomials #unique-factorization-domains
568
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How to prove that UFD implies normal?

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#abstract-algebra #commutative-algebra #unique-factorization-domains #integral-extensions
641
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Prove that $ k[x,y]/(x^3 - y^2)$ is not a UFD.

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#abstract-algebra #commutative-algebra #integral-domain #unique-factorization-domains
42
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Polynomial quotient rings over the integers and UFDs

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#abstract-algebra #unique-factorization-domains

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