Minimal elements under division in a ring
Posted by Caleb Stanford, at math.stackexchange.com,
Let $p$ be an element of a commutative ring with unity. The following definition is natural: $p$ is minimal under division if…
Why $0$ is not irreducible?
Posted by user778657, at math.stackexchange.com,
We took the following definition of irreducible: If $R$ is a commutative ring, $r \in R$ is irreducible if $r = ab$ for $a,b \in…
What is the correct notion of unique factorization in a ring?
Posted by Ishan Levy, at math.stackexchange.com,
I was recently writing some notes on basic commutative ring theory, and was trying to convince myself why it was a good idea to…
Is there a name for those elements $x$ of a commutative ring $R$ such that $Rx$ is maximal among all proper ideals?
Posted by goblin GONE, at math.stackexchange.com,
Ever since learning basic ring theory, I've always felt kind of confused about the fact that: maximal ideals are prime (because…