Difference between revisions of "Atomic lattice"
From Encyclopedia of Mathematics
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| − | 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]] 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. | 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". | Some authors use "atomic" to denote what is here defined as "atomistic". | ||
Latest revision as of 19:16, 4 January 2015
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
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