Vol. 31, No. 3, 1969

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On (m n) products of Boolean algebras

Robert Hamor La Grange, Jr.

Vol. 31 (1969), No. 3, 725–731

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
Received: 19 July 1968
Published: 1 December 1969
Robert Hamor La Grange, Jr.