New posts in Ring Theory

Why is it natural to define a prime as $p|ab$ implies $p|a$ or $p|b$?

Gaussian Integers form an Euclidean Ring

Primes in $\mathbb{Z}[\sqrt{2}]$?

Why doesn't the definition "$p$ is called 'prime' if $p\mid ab\implies p\mid a\,\text{ or }\,p\mid b$" hold up when we square numbers?

Coordinate ring of a scheme in functorial algebraic geometry

Non unique factorization of integer valued polynomials

$(x,y)\subset \mathbb Q[x,y]$ is not a principal ideal

How is the quotient of two ideals defined?

The group ring of a ring.

Let $\theta$ be a root of $p(x)=x^3+9x+6$, find the inverse of $1+\theta$ in $\mathbb{Q(\theta)}$