Vol. 33, No. 2, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Projective distributive lattices

Raymond Balbes and Alfred Horn

Vol. 33 (1970), No. 2, 273–279
Abstract

It will be shown that a countable distributive lattice is projective if and only if the product of any two join irreducible elements is join irreducible, and every element of the lattice is both a finite sum of join irreducible elements and a finite product of meet irreducible elements. For an arbitrary distributive lattice, necessary and sufficient conditions for projectivity are obtained by adding to these conditions a further condition on the set of join irreducible elements.

Mathematical Subject Classification
Primary: 06.50
Milestones
Received: 1 October 1969
Published: 1 May 1970
Authors
Raymond Balbes
Alfred Horn