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New posts in integral-domain
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
abstract-algebra
ring-theory
commutative-algebra
integral-domain
Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain. [duplicate]
abstract-algebra
ring-theory
integral-domain
polynomial-rings
Arithmetic structure including both unique factorization and Dedekind domains
abstract-algebra
ring-theory
integral-domain
unique-factorization-domains
dedekind-domain
Proving a Certain $\mathbb{C}$-Algebra is a Domain Using a Specified Method
abstract-algebra
commutative-algebra
integral-domain
unique-factorization-domains
Principal ideal rings that are not integral domains
abstract-algebra
ring-theory
principal-ideal-domains
integral-domain
Is it really necessary to work with the fraction field here?
polynomials
ring-theory
commutative-algebra
ideals
integral-domain
Prime $p\in R$ remains prime in $R[x]$ (Gauss's Lemma)
abstract-algebra
polynomials
ring-theory
integral-domain
GCD in Gaussian integers.
abstract-algebra
divisibility
integral-domain
Domain strictly contained in the intersection of localizations at the primes of height one
commutative-algebra
integral-domain
Is an infinite field always isomorphic to a non-trivial fraction field?
abstract-algebra
field-theory
integral-domain
Show that $A[X]/(aX+b)$ is an integral domain
abstract-algebra
polynomials
ring-theory
divisibility
integral-domain
In a noetherian integral domain every non invertible element is a product of irreducible elements
abstract-algebra
commutative-algebra
ring-theory
integral-domain
noetherian
Show that an integral domain with finitely many ideals is a field [duplicate]
abstract-algebra
ideals
integral-domain
Proof that in an integral domain every prime element is irreducible [duplicate]
abstract-algebra
ring-theory
proof-explanation
integral-domain
Is $\Bbb Z_4 [X]$ an integral domain?
abstract-algebra
integral-domain
polynomial-rings
Rings isomorphic to $\mathbb{Z}_6\times\mathbb{Z}_{10}$
abstract-algebra
ring-theory
integral-domain
A fraction field is not finitely generated over its subdomain
abstract-algebra
commutative-algebra
integral-domain
finitely-generated
In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?
abstract-algebra
ring-theory
gcd-and-lcm
integral-domain
Associates in Integral Domain
abstract-algebra
proof-verification
integral-domain
How to show every field is a Euclidean Domain.
abstract-algebra
field-theory
integral-domain
euclidean-algorithm
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