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Distributive Extensions and Quasi-Framal Algebras

Published online by Cambridge University Press:  20 November 2018

Tah-Kai Hu
Tah-Kai Hu*
Affiliation:
Southern Illinois University
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In (2; 3; 4), A. L. Foster denned Boolean extensions of framal algebras and bounded Boolean extensions of framal-in-the-small algebras. Foster proved that the class of Boolean (of bounded Boolean) extensions of a framal (a framal-in-the-small) algebra A is coextensive up to isomorphism with a certain class of subdirect powers of A, namely, the class of normal (of bounded normal) subdirect powers of A. His proofs apply, however, to considerably more general situations. Indeed, as remarked in (2), the construction of Boolean extensions may be carried out for an arbitrary universal algebra with finitary operations; this is done, in fact, in (4).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 265 - 281
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Birkhoff, G., Lattice theory (New York, 1948).Google Scholar
2. Foster, A. L., Generalized “Boolean” theory of universal algebras. I. Subdirect sums and normal representation theory, Math. Z., 58 (1953), 306–336.Google Scholar
3. Foster, A. L., Generalized “Boolean” theory of universal algebras. II. Identities and subdirect sums of functionally complete algebras, Math. Z., 59 (1953), 191–199.Google Scholar
4. Foster, A. L., Functional completeness in the small. Algebraic structure theorems and identities, Math. Ann., 148(1961), 29–58.Google Scholar