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On the Theory of Ring-Logics

Published online by Cambridge University Press:  20 November 2018

Adil Yaqub
Adil Yaqub*
Affiliation:
University of California, Berkeley and Purdue University
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Boolean rings (B, ✗, + ) and Boolean logics ( = Boolean algebras) (B, ∩, *) are equationally interdefinable in a familiar way (6). Foster's theory of ring-logics (1; 2; 3) raises this interdefinability and indeed the entire Boolean theory to a more general level. In this theory a ring (or an algebra) R is studied modulo K, where K is an arbitrary transformation group (or “Coordinate transformations”) in R.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 323 - 328
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Foster, A. L., On n-ality theories in rings and their logical algebras, including tri-ality principle in three-valued logics, Amer. J. Math., 72 (1950), 101–123.Google Scholar
2. Foster, A. L., p-;rings and ring-logics, Univ. Calif. Publ., 1 (1951), 385–396.Google Scholar
3. Foster, A. L., pk-rings and ring-logics, Ann. Scu. Norm. Pisa, 5 (1951), 279–300.Google Scholar
4. Foster, A. L., Unique subdirect factorization within certain classes of universal algebras, Math. Z., 62 (1955), 171–188.Google Scholar
5. McCoy, N. H. and Montgomery, D., A representation of generalized Boolean rings, Duke Math. J., 3 (1937), 455–459.Google Scholar
6. Stone, M. H., The theory of representations of Boolean algebras, Trans. Amer. Math. Soc, 40 (1936), 37–111.Google Scholar