Definition:Join-Irreducible Element

Definition

Let $\struct{S, \vee, \preceq}$ be a join semilattice.

Let $z \in S$.

Then $z$ is said to be join-irreducible if and only if

$\forall x, y \in S : z \preceq x \vee y \implies z \preceq x$ or $z \preceq y$

Also see

• Definition:Meet-Irreducible Element

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.