# Atomic lattice

From Encyclopedia of Mathematics

The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

2020 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://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