New posts in ring-theory

Under what conditions will the ring homomorphism $\phi : R \to S$ satisfy the following results about prime and maximal ideals?

Does a homomorphism from a unital ring to an integral domain force a multiplicative identity?

Algebras that are free modules over a subalgebra

The ring $\mathbb{C}[x,y]/\langle xy \rangle$

Show that $(2+i)$ is a prime ideal

Exhibit the ideals of $\mathbb{Z}[x]/(2,x^3+1)$

Why define vector spaces over fields instead of a PID?

Commutative integral domain with d.c.c. is a field [duplicate]

In a matrix ring, no zero divisors may have an inverse

Do both versions (invariant and primary) of the Fundamental Theorem for Finitely Generated Abelian Groups hold at the same time?

Showing two polynomial rings over $\mathbb{C}$ aren't isomorphic

How to prove $e^{A \oplus B} = e^A \otimes e^B$ where $A$ and $B$ are matrices? (Kronecker operations)

Can we make an integral domain with any number of members?

Problem in the "proof" of Eisenstein's criterion on irreducibility.

Prove that $I \subseteq R$ is prime if and only if $R/I$ is an integral domain.

$\exists x \in R$ and $\exists n \in\mathbb{N}$ such that $x^{n+1} = x^n \implies x^2 = x$

Show that $(p,\sqrt{d})$ is a prime ideal in $Z[\sqrt{d}]$

Suppose R is a commutative ring, M is the maximum ideal of R, and R/M is not a field. Prove: (R/M)² = 0.

Characterize finite dimensional algebras without nilpotent elements

Consequence of Nakayama Lemma's to Local Rings