Vol. 27, No. 2, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
On abelian pseudo lattice ordered groups

J. Roger Teller

Vol. 27 (1968), No. 2, 411–419
Abstract

Throughout this paper po-group will mean partially ordered abelian group. A subgroup H of a po-group G is an o-ideal if H is a convex, directed subgroup of G. A subgroup M of G is a value of 0g G if M is an o-ideal of G that is maximal without g. Let (g) = {M GM is a value of g} and (g) = ∩ℳ(g). Two positive elements a,b G are pseudo disjoint (p-disjoint) if a ∈ℳ(b) and b ∈ℳ(a), and G is a pseudo-lattice ordered group (pl-group) if each g G can be written g = ab where a and b are p-disjoint.

The main result of §2 shows that every pl-group G is a Riesz group. That is, G is semiclosed (ng 0 implies g 0 for all g G and all positive integers n), and G satisfies the Riesz interpolation property; if, whenever x1,,xm, y1,,yn are elements of G and xi yj for 1 i m, 1 j n, then there is an element z G such that xi z yj.

Mathematical Subject Classification
Primary: 06.78
Milestones
Received: 3 July 1967
Published: 1 November 1968
Authors
J. Roger Teller