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Show that $\sqrt{-n}$ and $\sqrt{-n} +1$ are not prime in $\mathbb{Z}[\sqrt{-n} ]$

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#abstract-algebra #ring-theory #unique-factorization-domains
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Show that every prime ideal of A (UFD) is generated by a set of prime elements

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#abstract-algebra #maximal-and-prime-ideals #unique-factorization-domains
381
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In UFD every irreducible element is prime

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#ring-theory #unique-factorization-domains
65
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Help with unique factorization domains

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#abstract-algebra #unique-factorization-domains
201
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Is the polynomial ring of elementary symmetric polynomials involving n variables over a field is integrally closed?

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#polynomials #commutative-algebra #field-theory #unique-factorization-domains #integral-extensions
152
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Integer solutions for $\frac{n(n-1)}2=m^2-1$

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#number-theory #diophantine-equations #unique-factorization-domains #pell-type-equations #triangular-numbers
258
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Unique factorization domain and principal ideal

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87
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Exercise 0.9 in Miles Reid's Commutative Algebra

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47
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Reducibility of multi-variable polynomials

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#abstract-algebra #ring-theory #irreducible-polynomials #unique-factorization-domains
49
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Why a polynomial is irreducible over Z

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#polynomials #field-theory #irreducible-polynomials #unique-factorization-domains
351
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Coordinate rings of projective varieties as UFDs

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#algebraic-geometry #algebraic-curves #unique-factorization-domains
84
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Localizations of $k[y,z]/(1-y^2+z^2)$ UFDs

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#algebraic-geometry #ring-theory #commutative-algebra #unique-factorization-domains #local-rings
68
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An example of a local ring of $V$ at $p$ not ufd

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#algebraic-geometry #unique-factorization-domains #local-rings
124
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Localizations of $k[x,y]/(f)$ UFD

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#abstract-algebra #polynomials #ring-theory #commutative-algebra #unique-factorization-domains
679
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Every irreducible is product of irreducibles

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#abstract-algebra #unique-factorization-domains

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