New posts in ring-theory

Let $H=(1+i)\mathbb{Z}[i]$. Let $f:\mathbb{Z}\to \mathbb{Z}[i]/H : f(z)=[z]$. Prove $\ker f=2\mathbb{Z}$.

abstract-algebra ring-theory ideals ring-homomorphism

Every ideal in $\mathbb{Z}[\sqrt d]$ is finitely generated by at most two elements of the form $a, b + c \sqrt d$

abstract-algebra ring-theory ideals

Discuss $\mathbb R[X]/(aX^2 +bX + c)$ in terms of $\Delta = b^2-4ac$

abstract-algebra polynomials ring-theory irreducible-polynomials quotient-group

Proving a ring in which $r^n=r$ for all $r$ is commutative.

abstract-algebra ring-theory

Example of a finitely generated faithful torsion module over a commutative ring

abstract-algebra ring-theory commutative-algebra

Prove that if $I$ is a prime ideal of $R$, then $I[x]$ is a prime ideal of $R[x]$

abstract-algebra polynomials ring-theory commutative-algebra

Ring of formal power series over a principal ideal domain is a unique factorisation domain

abstract-algebra ring-theory principal-ideal-domains noetherian unique-factorization-domains

Radical/Prime/Maximal ideals under quotient maps

abstract-algebra commutative-algebra ring-theory ideals

Prove $\ker \phi=\langle 1+\sqrt{-5}, 2\rangle$

abstract-algebra ring-theory ring-homomorphism

Lemma on infinitely generated projective modules

ring-theory modules projective-module

Normality condition for a DVR

abstract-algebra ring-theory commutative-algebra

Have I found a counterexample to Noether-Skolem? (No, but I am confused...)

abstract-algebra ring-theory noncommutative-algebra

An example of a noncommutative PID

ring-theory modules examples-counterexamples

$x \otimes y - y \otimes x \neq 0$ in $I \otimes_{R} I$

abstract-algebra ring-theory tensor-products

Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$.

ring-theory

Is $2$ not a prime (in $\Bbb R$)?

abstract-algebra ring-theory

History of the terms "prime" and "irreducible" in Ring Theory.

ring-theory terminology math-history

Ring homomorphism where $g(1)$ is not identity

ring-theory ring-homomorphism

Must this rng be a ring?

abstract-algebra ring-theory rngs

Homomorphisms from a unital ring to a ring with no zero divisors preserve unity?

abstract-algebra ring-theory