Irreducible element
= Irreducible element
{wiki=Irreducible_element}
In the context of abstract algebra, particularly in the study of partially ordered sets and rings, an **irreducible element** has a specific definition: 1. **In a Partially Ordered Set**: An element \\( x \\) in a partially ordered set \\( P \\) is called irreducible if it cannot be expressed as the meet (greatest lower bound) of two elements from \\( P \\) unless one of those elements is \\( x \\) itself.