The Completion of a Lattice Ordered Group
- 1 February 1969
- journal article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 9 (1-2) , 182-208
- https://doi.org/10.1017/s1446788700005760
Abstract
A lattice ordered group(‘l-group’) is calledcompleteif each set of elements that is bounded above has a least upper bound (and dually). A completel-group is archimedean and hence abelian, and each archimedeanl-group has a completion in the sense of the following theorem.Keywords
This publication has 20 references indexed in Scilit:
- Complete distributivity in lattice-ordered groupsPacific Journal of Mathematics, 1967
- Free lattice-ordered abelian groups. IIMathematische Annalen, 1965
- The relationship between the radical of a lattice-ordered group and complete distributivityPacific Journal of Mathematics, 1964
- Free lattice-ordered Abelian groupsMathematische Annalen, 1963
- Completely distributed lattice-ordered groupsPacific Journal of Mathematics, 1962
- Über Strukturverbände von VerbandsgruppenActa Mathematica Hungarica, 1962
- Prime Ideals in Vector LatticesCanadian Journal of Mathematics, 1962
- Some Structure Theorems for Lattice-Ordered GroupsTransactions of the American Mathematical Society, 1961
- Partially Ordered SetsTransactions of the American Mathematical Society, 1937
- Partially ordered setsTransactions of the American Mathematical Society, 1937