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Every irreducible element is prime: always holds under surjective ring homomorphism?

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449
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Proof for Unique Factorization Domain

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#abstract-algebra #ring-theory #principal-ideal-domains #unique-factorization-domains
363
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Possible Irreducible but NOT prime!

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#abstract-algebra #unique-factorization-domains
1.3k
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Coordinate ring of the unit circle is never a UFD?

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#abstract-algebra #commutative-algebra #algebraic-curves #unique-factorization-domains
195
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Does Shor's algorithm work for noncommutitive or nonassociative algebras?

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#number-theory #algebraic-number-theory #quaternions #prime-factorization #unique-factorization-domains
40
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How to determine this solutions?

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844
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Definition of improper divisor in algebra

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905
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What does it mean for a factorization to be unique up to unit factors?

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235
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If $R$ is a noetherian local ring, then every 2-generated ideal has finite projective dimension iff $R$ is a UFD

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#ring-theory #commutative-algebra #homological-algebra #projective-module #unique-factorization-domains
183
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How do I work out the last sentence in this section of a proof of the Unique Factorization Theorem?

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#proof-verification #factoring #unique-factorization-domains
98
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help ! discriminant of a polynomial

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#number-theory #unique-factorization-domains
544
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UFD yields height of certain primes at most $1$

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1.8k
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Normal if and only if is UFD

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#commutative-algebra #irreducible-polynomials #unique-factorization-domains
294
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Elements as a product of unit and power of element in UFD

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#abstract-algebra #unique-factorization-domains
79
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Let $R$ be a UFD and $p,q,r \in R$. $pq=r^3$ and $\gcd(p,q)=1$ then $p,q$ are cubes up to associates.

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