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15
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Determining ring type for the formal series ring

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#abstract-algebra #ring-theory #power-series #principal-ideal-domains #unique-factorization-domains
63
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When an irreducible $d \in D$ remains irreducible in $D[T]/(p)$?

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#abstract-algebra #commutative-algebra #unique-factorization-domains
235
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Show that the following localization is a unique factorization domain

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#ring-theory #localization #unique-factorization-domains
617
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Is there a constructive proof that a Euclidean domain is a UFD?

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#abstract-algebra #ring-theory #unique-factorization-domains
201
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Contradiction of Unique Factorization Theorem

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#abstract-algebra #irreducible-polynomials #unique-factorization-domains
166
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Check whether $\mathbb{Q}[X_{1},X_{2},...]/(f_{1},f_{2},...)$ is a Bézout domain, Noetherian, Factorial, or PID

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#abstract-algebra #ring-theory #principal-ideal-domains #noetherian #unique-factorization-domains
359
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characterization of unique factorization domain

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#abstract-algebra #integral-domain #unique-factorization-domains
267
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How can we have an irreducible element in a UFD?

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#abstract-algebra #ring-theory #unique-factorization-domains
481
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Can an integral domain have an element that has no square root but has a square root in the field of fractions?

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#abstract-algebra #number-theory #ring-theory #examples-counterexamples #unique-factorization-domains
709
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For which value of $n$ the ring $\mathbb{Z}[\sqrt{n}]$ is a UFD?

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#abstract-algebra #number-theory #unique-factorization-domains
805
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Localization preserves UFDs using Kaplansky criterion

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#abstract-algebra #localization #unique-factorization-domains
107
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Polynomial on Unique Factorization Domain

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#ring-theory #irreducible-polynomials #unique-factorization-domains
48
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On inverting in non-UFDs

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#number-theory #modular-arithmetic #algebraic-number-theory #inverse #unique-factorization-domains
565
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How can I show that $ab \sim \gcd (a,b) {\operatorname{lcm} (a,b)}$ for any $a,b \in R \setminus \{0\}$?

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#abstract-algebra #ring-theory #unique-factorization-domains
129
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How can I show that in a UFD $\operatorname{gcd} (ra,rb) \sim r \operatorname{gcd} (a,b)$?

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#abstract-algebra #ring-theory #unique-factorization-domains

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