Free Vector Lattices
- 1 January 1968
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 20, 58-66
- https://doi.org/10.4153/cjm-1968-008-x
Abstract
This note presents a useful explicit characterization of the free vector lattice FVL(ℵ) on ℵ generators as a vector lattice of piecewise linear, continuous functions on Rℵ, where ℵ is any cardinal and R is the set of real numbers. A transfinite construction of FVL(ℵ) has been given by Weinberg (14) and simplified by Holland (13, § 5). Weinberg's construction yields the fact that FVL(ℵ) is semi-simple; the present characterization is obtained by combining this fact with a theorem from universal algebra due to Garrett Birkhoff.Keywords
This publication has 1 reference indexed in Scilit:
- Structure and decomposition theory of latticesProceedings of Symposia in Pure Mathematics, 1961