Vol. 31, No. 3, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
On (m n) products of Boolean algebras

Robert Hamor La Grange, Jr.

Vol. 31 (1969), No. 3, 725–731
Abstract

This discussion begins with the problem of whether or not all (m n) products of an indexed set {At}tT of Boolean algebras can be obtained as m-extensions of a particular algebra n. The construction of n is similar to the construction of the Boolean product of {At}tT; however the 𝒜t are embedded in n in such a way that their images are n-independent. If there is a cardinal number n, satisfying n < nm, then (mn) products are not obtainable in this manner. For the case n = m an example shows the answer to be negative. It is explained how the class of m-extensions of n is situated in the class of all (m n) products of {At}tT. A set of m-representable Boolean algebras is given for which the minimal (m n) product is not m-representable and for which there is no smallest (m n) product.

Mathematical Subject Classification
Primary: 06.60
Milestones
Received: 19 July 1968
Published: 1 December 1969
Authors
Robert Hamor La Grange, Jr.