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Integral-domain
New post in Integral-domain
Finite integral domain
February 4th, 2020
finite-fields
abstract-algebra
finite-rings
integral-domain
ring-theory
Maximal value of domain for a function by looking at inverse function.
August 1st, 2022
functions
integral-domain
calculus
algebra-precalculus
inverse
Show the set of GCD's of two elements in an integral domain is the set of associates of their GCD
October 23rd, 2020
abstract-algebra
ring-theory
integral-domain
Field of Quotients Explanation
August 1st, 2022
integral-domain
abstract-algebra
field-theory
Definition of irreducible element.
August 1st, 2022
abstract-algebra
ring-theory
integral-domain
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
August 3rd, 2020
abstract-algebra
integral-domain
ring-theory
Let $D$ be a principal ideal domain. Show that every proper ideal of $D$ is contained in a maximal ideal of $D$.
April 16th, 2020
abstract-algebra
integral-domain
ring-theory
use the definition for an integral domain to prove that Z7 is an integral domain
February 24th, 2020
abstract-algebra
integral-domain
ring-theory
Prove or disprove that the ring $\mathbb{Z}[x]/(x^2-1)$ is an integral domain
April 20th, 2020
abstract-algebra
ring-theory
integral-domain
How to determine the interval for integration?
February 13th, 2020
integration
integral-domain
calculus
Principal prime ideal is generated by irreducible element
August 1st, 2022
ideals
integral-domain
abstract-algebra
ring-theory
Order of an element in an integral domain
August 1st, 2022
abstract-algebra
integral-domain
ring-theory
Irreducible elements and Associates
March 24th, 2020
integral-domain
proof-writing
ring-theory
Proving that any finite integral domain is a field.
June 3rd, 2020
alternative-proof
abstract-algebra
integral-domain
Identifying units in a polynomial ring
March 15th, 2020
ring-theory
integral-domain
proof-explanation
abstract-algebra
polynomials
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
August 1st, 2022
integral-domain
abstract-algebra
proof-verification
proof-writing
Prove the fractional field of an integral domain is the smallest field containing the integral domain
August 1st, 2022
field-theory
integral-domain
abstract-algebra
Meaning of $Z\oplus Z$
June 17th, 2020
direct-sum
integral-domain
ring-theory
When does sum of two units give a unit?
December 25th, 2020
integral-domain
abstract-algebra
A question about the relation between division ring and domain
August 1st, 2022
abstract-algebra
ring-theory
integral-domain
If $R$ is an integral domain, then $(R[x])^\times=R^\times$
August 1st, 2022
polynomials
abstract-algebra
integral-domain
proof-verification
ring-theory
Noetherian ring and prime ideal contained in an invertible maximal ideal.
October 28th, 2020
commutative-algebra
ideals
integral-domain
noetherian
Example of finite field extension where root not separable
August 1st, 2022
abstract-algebra
ring-theory
field-theory
extension-field
integral-domain
The characteristic of a subdomain is the same as the integral domain in which it is contained?
February 8th, 2020
integral-domain
abstract-algebra
Specific way of showing $\Bbb Z[\sqrt{-d}]$ is not a Euclidean Domain when $d>2$
August 1st, 2022
field-theory
principal-ideal-domains
integral-domain
ring-theory
abstract-algebra
Prime ideal and maximal ideal of an integral domain
August 1st, 2022
ring-theory
integral-domain
maximal-and-prime-ideals
abstract-algebra
Prime ideal in a polynomial ring over an integrally closed domain
December 2nd, 2020
abstract-algebra
ideals
commutative-algebra
integral-domain
$P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
November 14th, 2020
maximal-and-prime-ideals
abstract-algebra
proof-writing
ideals
integral-domain
On an integral domain, with $(m,n)=1$, $a^m = b^m$ and $a^n = b^n$ implies $a=b$.
September 14th, 2020
abstract-algebra
ring-theory
integral-domain
Prove that $\mathbb{Z}[i]$ is an integral domain.
August 1st, 2022
ring-theory
proof-verification
integral-domain
gaussian-integers
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