Definition:Irreducible Element of Ring

Definition
Let $\struct {D, +, \circ}$ be an integral domain whose zero is $0_D$.

Let $\struct {U_D, \circ}$ be the group of units of $\struct {D, +, \circ}$.

Let $x \in D: x \notin U_D, x \ne 0_D$, that is, $x$ is non-zero and not a unit.

Also see

 * Equivalence of Definitions of Irreducible Element of Ring


 * Definition:Irreducible Ring
 * Definition:Prime Element of Ring

Special cases

 * Definition:Irreducible Polynomial