# Atomic lattice

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 06B [MSN][ZBL]

A lattice with a zero $0$ in which, for each non-zero element $a$, there exists an atom $p\leq a$, that is, $0 < p$ and $x < p \Rightarrow x=0$

A lattice is **atomistic** if it is atomic and every element is a join of some finite set of atoms.

Some authors use "atomic" to denote what is here defined as "atomistic".

**How to Cite This Entry:**

Atomic lattice.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Atomic_lattice&oldid=36083

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article