Atomic lattice
From Encyclopedia of Mathematics
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=32605
Atomic lattice. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Atomic_lattice&oldid=32605
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article