Let \(R\) be a commutative ring. A nonzero element \(r\in R\) that is not a unit is irreducible if for all \(a,b\in R\), \[ r=ab \implies a \in R^{\times} \text{ or } b\in R^{\times}. \]
Irreducible element
D-TO3IY
D-TO3IY
Let \(R\) be a commutative ring. A nonzero element \(r\in R\) that is not a unit is irreducible if for all \(a,b\in R\), \[ r=ab \implies a \in R^{\times} \text{ or } b\in R^{\times}. \]