Bibliography
Stone, M. H.: The theory of representations of Boolean algebras. Trans. Amer. Math. Soc.40, 37–111 (1936).
McCoy, N. H., andDeane Montgomery: A representation of generalized Boolean rings. Duke Math. J.3, 455–459 (1937.
McCoy, N. H.: Subdirect sums of rings. Bull. Amer. Math. Soc.53, 856–877 (1947).
Rosenbloom, P.: The Elements of Mathematical Logic. The Dover Series (1950).
Wade, L. I.: Post algebras and rings. Duke Math. J.12, 389–395 (1945).
Birkhoff, G.: Subdirect unions in universal algebras. Bull. Amer. Math. Soc.50, 764–768(1944).
Foster, A. L.: Generalized “Boolean” theory of universal algebras, Part I: Subdirect sums and normal representation theorem. Math. Z.58, 306–336 (1953), and Part II: Identities and subdirect sums of functionally complete algebras. Math. Z.59, 191–199 (1953).
Foster, A. L.: The identities of—and unique subdirect factorization within—classes of universal algebras. Math. Z.62, 171–188 (1955).
Foster, A. L.: The idempotent elements of a commutative ring form a Boolean algebra; ring duality and transformation theory. Duke Math. J.12, 143–152 (1945).
Foster, A. L.: Onn-ality theories in rings and their logical algebras, etc. Amer. J. Math.72 101–123 (1950).
Foster, A. L.:p-Rings and their Boolean-vector representation. Acta Math. Stockh.84, 231–261 (1950).
Foster, A. L.:p-Rings and ring logics. Univ. California Publ. Math.1, 385–396 (1951).
Yaqub, A.: On the theory of ring-logics and universal algebras. Doctoral dissertation, Univ. of California, Berkeley, (1955).
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Foster, A.L. Ideals and their structure in classes of operational algebras. Math Z 65, 70–75 (1956). https://doi.org/10.1007/BF01473870
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DOI: https://doi.org/10.1007/BF01473870