Newbetuts

If $I$ is a finitely generated ideal of $A[X]$, is $I\cap A$ necessarily finitely generated for a commutative unital ring $A$?

Polynomial rings -- Inherited properties from coefficient ring

Converting a polynomial ring to a numerical ring (transport of structure)

Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.

Is the ring of formal power series in infinitely many variables a unique factorization domain?

fraction field of the integral closure

Isomorphism of rings implies isomorphism of vector spaces?

gcd in principal ideal domain

How do I see that every left ideal of a square matrix ring over a field is principal?

$R/I$ is not Noetherian. Prove that $I$ is a prime ideal.

Rig in which 0 is not an absorber.

How can one visualize a homomorphic mapping.

Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$

If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$ [duplicate]

List of prime numbers in imaginary quadratic fields with UFD

What are the semisimple $\mathbb{Z}$-modules?

New posts in ring-theory

Does this "extension property" for polynomial rings satisfy a universal property?

Artinian if and only if Noetherian

Why is the absence of zero divisors not sufficient for a field of fractions to exist?

$R$ with an upper bound for degrees of irreducibles in $R[x]$

If $I$ is a finitely generated ideal of $A[X]$, is $I\cap A$ necessarily finitely generated for a commutative unital ring $A$?

Polynomial rings -- Inherited properties from coefficient ring

Converting a polynomial ring to a numerical ring (transport of structure)

Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.

Is the ring of formal power series in infinitely many variables a unique factorization domain?

fraction field of the integral closure

Isomorphism of rings implies isomorphism of vector spaces?

gcd in principal ideal domain

How do I see that every left ideal of a square matrix ring over a field is principal?

$R/I$ is not Noetherian. Prove that $I$ is a prime ideal.

Rig in which 0 is not an absorber.

How can one visualize a homomorphic mapping.

Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$

If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$ [duplicate]

List of prime numbers in imaginary quadratic fields with UFD

What are the semisimple $\mathbb{Z}$-modules?