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New posts in integral-domain
If D is an Integral Domain and has finite characteristic p, prove p is prime.
abstract-algebra
proof-verification
integral-domain
$P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
abstract-algebra
proof-writing
ideals
maximal-and-prime-ideals
integral-domain
Prime ideal in a polynomial ring over an integrally closed domain [closed]
abstract-algebra
commutative-algebra
ideals
integral-domain
Prove that if $R$ is an integral domain and has ACCP, then $R[X]$ has ACCP
abstract-algebra
ring-theory
integral-domain
Irreducible elements for a commutative ring that is not an integral domain
abstract-algebra
commutative-algebra
integral-domain
Is there an Integral domain that is a GCD domain but NOT a UFD? [duplicate]
commutative-algebra
divisibility
integral-domain
unique-factorization-domains
gcd-and-lcm
Looking for an example of a GCD domain which is not a UFD
commutative-algebra
divisibility
integral-domain
unique-factorization-domains
gcd-and-lcm
Prove that an infinite ring with finite quotient rings is an integral domain
abstract-algebra
ring-theory
integral-domain
Prove that $p^2$ is the principal ideal $(2)$.
abstract-algebra
ideals
integral-domain
What is the fraction field of $R[[x]]$, the power series over some integral domain?
commutative-algebra
power-series
integral-domain
For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$? [duplicate]
ring-theory
gcd-and-lcm
integral-domain
Example of FD not satisfying ACCP
ring-theory
commutative-algebra
integral-domain
An integral domain $A$ is exactly the intersection of the localisations of $A$ at each maximal ideal
commutative-algebra
ideals
integral-domain
localization
Can infinitely many primes lie over a prime?
abstract-algebra
commutative-algebra
integral-domain
Integral domain that is not a factorization domain
abstract-algebra
ring-theory
commutative-algebra
integral-domain
Prove that in any GCD domain every irreducible element is prime
abstract-algebra
proof-explanation
integral-domain
Where Fermat's last theorem fails
abstract-algebra
number-theory
elementary-number-theory
integral-domain
unique-factorization-domains
How to prove that the Frobenius endomorphism is surjective?
abstract-algebra
field-theory
integral-domain
A subring of the field of fractions of a PID is a PID as well.
abstract-algebra
commutative-algebra
ring-theory
principal-ideal-domains
integral-domain
$a^m=b^m$ and $a^n=b^n$ imply $a=b$ [closed]
abstract-algebra
ring-theory
integral-domain
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