Atomic lattice

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