Vol. 21, No. 3, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Order sums of distributive lattices

Raymond Balbes and Alfred Horn

Vol. 21 (1967), No. 3, 421–435

In this paper, the authors define the orde r sum of a family of distributive lattices which is indexed by a partially ordered set P. The order sum reduces to the free product when P is trivially ordered, and to the ordinal sum when P is simply ordered.

It is proved that the order sum of conditionally implicative lattices is conditionally implicative, and that every projective distributive lattice is conditionally implicative. The second half of the paper investigates conditions under which the order sum of projective lattices is projective. It is shown that if {Lα|α P} is a family of distributive lattices having largest and smallest elements, then the order sum of the family is projective if and only if each Lα is projective, and P is such that the order sum of the family {Mα|α P} of one-element lattices Mα is projective.

Mathematical Subject Classification
Primary: 06.50
Received: 22 August 1966
Published: 1 June 1967
Raymond Balbes
Alfred Horn