Let \(R\) be a commutative ring. A nonzero element \(p\in R\) that is not a unit is prime if for all \(a,b \in R\), \[ p\divides ab \implies p\divides a \text{ or } p\divides b, \] where \(\divides\) denotes divisibility.
Prime element
D-AWSKI
D-AWSKI
Let \(R\) be a commutative ring. A nonzero element \(p\in R\) that is not a unit is prime if for all \(a,b \in R\), \[ p\divides ab \implies p\divides a \text{ or } p\divides b, \] where \(\divides\) denotes divisibility.