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Rings in Boolean algebras. (English) Zbl 0281.06007


MSC:

06E05 Structure theory of Boolean algebras
13-XX Commutative algebra
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References:

[1] Bernstein, B. A., Operations with respect to which the elements of a Boolean algebra form a group, Trans. Am. Math. Soc., 26, 171-175 (1924) · JFM 50.0629.08
[2] Bernstein, B. A., On the existence of fields in Boolean algebras, Trans. Am. Math. Soc., 28, 654-657 (1926) · JFM 52.0135.04
[3] Cunkle, C. H., A note on Boolean operations, Portugal. Math., 18, 177-179 (1959) · Zbl 0111.02402
[4] Elliot, J. G., Autometrization and the symmetric difference, Canad. J. Math., 5, 324-331 (1953) · Zbl 0052.26503
[5] Ellis, D., Autometrized Boolean algebras II, The group of motions of B, Canad. J. Math., 3, 145-147 (1951) · Zbl 0043.03401
[6] Frink, O., The operations of Boolean algebras, Ann. Math., 26, 477-490 (1927) · JFM 52.0135.03
[7] Frink, O., On the existence of linear algebras in Boolean algebras, Bull. Am. Math. Soc., 34, 329-333 (1928) · JFM 54.0162.04
[8] Grätzer, G., On Boolean functions. (Notes on lattice theory II), Rev. Math. Pures Appl., 7, 693-697 (1962) · Zbl 0134.25801
[9] Grâtzer, G.; Schmidt, E. T., Ideals and congruence relations in lattices, Acta Math. Acad. Sci. Hungar., 9, 137-175 (1958) · Zbl 0085.02002
[10] Rudeanu, S., On the determination of Boolean algebras by means of binary operations, Rev. Math. Pures Appl., 6, 171-183 (1961), (in Russian)
[11] Rudeanu, S., Sur quelques applications des équations booléennes, (Moisil, Gr. C., Logique, Automatique, Informatique (1971), Editura Academie R.S. România: Editura Academie R.S. România New York), 177-193
[12] Vaidyanathaswamy, R., On the group of operations of a Boolean algebra, J. Indian Math. Soc., 2, 250-254 (1937) · JFM 63.0026.03
[13] Wiener, N., Certain formal invariances in Boolean algebras, Trans. Am. Math. Soc., 18, 65-72 (1917) · JFM 46.0092.02
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