Definition:Atom of Lattice

Definition
Let $\struct {S, \vee, \wedge, \preceq}$ be a lattice.

An atom of $\struct {S, \vee, \wedge, \preceq}$ is an element $A \in S$ such that:
 * $\forall B \in S: B \preceq A, B \ne A \implies B = \bot$
 * $A \ne \bot$

where $\bot$ denotes the bottom of $\struct {S, \vee, \wedge, \preceq}$.