Abstract
In the last decades various generalisations of the notion of boolean algebra have emerged. Let us just mention the de Morgan algebras and the Stone algebras.
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References
M. E. Adams, Principal congruences in de Morgan algebras, Proc. Edinburgh Math. Soc. 30 (1987), 415–421.
M. E. Adams and H. A. Priestley, Kleene algebras are almost universal. Preprint.
R. Balbes and P. Dwinger, Distributive lattices, University of Missouri Press, Columbia, Missouri, 1974.
R. Beazer, On some small varieties of distributive Ockham algebras, Glasgow Math. J. 25 (1984), 175–181.
R. Beazer, Injectives in some small varieties of Ockham algebras, Glasgow J. Math. 25 (1984), 183–191.
R. Beazer, Congruence pairs for algebras abstracting Kleene and Stone algebras, Czechoslovak Math. J. 35 (1985), 260–268.
J. Berman, Distributive lattices with an additional unary operation, Aequationes Math. 16 (1977), 165–171.
T. S. Blyth and J. C. Varlet, On a common abstraction of de Morgan algebras and Stone algebras, Proc. Roy. Soc. Edinburgh 94 (1983), 301–308.
T. S. Blyth and J. C. Varlet, Subvarieties of the class of MS-algebras, Proc. Roy. Soc. Edinburgh 95 (1983), 157–169.
T. S. Blyth and J. C. Varlet, Fixed points in MS-algebras, Bull. Soc. Roy. Sci. Liège 53 (1984), 3–8.
T. S. Blyth and J. C. Varlet, Congruences on MS-algebras, Bull. Soc. Roy. Sci. Liège 53 (1984) 341–362.
T. S. Blyth and J. C. Varlet, MS-algebras definable on a distributive lattice, Bull. Soc. Roy. Sci. Liège 54 (1985), 167–182.
T. S. Blyth and J. C. Varlet, The ideal lattice of an MS-algebra, Glasgow Math. J. 30 (1988), 137–143.
T. S. Blyth and J. C. Varlet, Sur la construction de certaines MS-algebres, Portugaliae Math. 39 (1980), 489–496.
T. S. Blyth and J. C. Varlet, Corrigendum Sur la construction de certaines MS-algebres, Portugaliae Math. 42 (1983-1984), 469–471.
T. S. Blyth, A. S. A. Noor and J. C. Varlet, Ockham algebras with de Morgan skeletons, Journal of Algebra 117 (1988), 165–178.
T. S. Blyth, P. Goossens and J. C. Varlet, MS-algebras arising from fences and crowns, to appear in Contributions to General Algebra 6, Vienna.
T. S. Blyth and J. C. Varlet, On the dual space of an MS-algebra, to appear in Mathematica Pannonica.
W. H. Cornish, Antimorphic action, Research and Exposition in Mathematics, 12, Heldermann Verlag, Berlin, 1986.
B. A. Davey, On the lattice of subvarieties, Houston J. Math. 5 (1979), 183–192.
B. A. Davey and H. A. Priestley, Generalised piggyback dualities and applications to Ockham algebras, Houston J. Math., to appear.
M. S. Goldberg, Distributive p-algebras and Ockham algebras: a topological approach, Ph. D. Thesis, La Trobe University, Australia, 1979.
M. S. Goldberg, Distributive Ockham algebras: free algebras and injectivity, Bull. Austral. Math. Soc. 24 (1981), 161–203.
G. Grätzer, Lattice theory: first concepts and distributive lattices, Freeman, San Francisco, California, 1971.
T. Katrinak and K. Mikula, On a construction of MS-algebras, Portugaliae Math. 45 (1988), 157–163.
H. Lakser, Principal congruences of pseudocomplemented distributive lattices, Proc. Amer. Math. Soc. 37 (1973), 32–36.
H. A. Priestley, The construction of spaces dual to pseudocomplemented distributive lattices, Quart. J. Math. Oxford 26 (1975), 215–228.
H. A. Priestley, Ordered sets and duality for distributive lattices, Ann. Discrete Math. 23 (1984), 39–60.
M. Ramalho and M. Sequeira, On generalized MS-algebras, Portugaliae Math. 44 (1987), 315–328.
H. P. Sankappanavar, A characterization of principal congruences of de Morgan algebras and its applications, Math. Logic in Latin America, North-Holland, 1980.
H. P. Sankappanavar, Distributive lattices with a dual endomorphism, Z. Math. Logik Grundlag. Math. 31 (1985), 385–392.
D. Schweigert and M. Szymanska, On distributive correlation lattices, Coll. Math. Soc. Janos Bolyai 33 (1980), 697–721.
M. Sequeira, Varieties of Ockham algebras satisfying x≤f 4 (x), Portugaliae Math. 45 (1988), 369–391.
A. Urquhart, Distributive lattices with a dual homomorphic operation, Studia Logica 38 (1979), 201–209.
J. Vaz de Carvalho, The subvariety K 2, 0 of Ockham algebras, Bull. Soc. Roy. Sci. Liège 53 (1984), 393–400.
J. Vaz de Carvalho, Congruences on algebras of K n,0, Bull. Soc. Roy. Sci. Liège 54 (1985), 301–303.
J. Vaz de Carvalho, Sobre as variedades Kn, 0 e álgebras de Lukasiewicz generalizadas, Ph. D. Thesis, Universida.de de Lisboa (1986).
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Varlet, J.C. (1990). MS-Algebras: a Survey. In: Almeida, J., Bordalo, G., Dwinger, P. (eds) Lattices, Semigroups, and Universal Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2608-1_30
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DOI: https://doi.org/10.1007/978-1-4899-2608-1_30
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