Abstract
Distributive double p-algebras and regular double p-algebras are shown to have the amalgamation property (AP). Finitely generated varieties of distributive double p-algebras with the AP are characterized, and also varieties generated by algebras with a bounded finite number of maximal or minimal prime ideals.
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Banaschewski, B.,Injectivity and essential extensions in equational classes of algebras, inProc. Conf. Universal Algebra, Queen's Univ., Kingston 1969, Queen's Papers in Pure and Applied Math., Kingston, Ontario, 1970, pp. 131–147.
Beazer, R.,The determination congruence on double p-algebras, Algebra Universalis6 (1976), 121–129.
Burris, S. andSankappanavar, H. P.,A Course in Universal Algebra, Springer-Verlag, New York Heidelberg Berlin, 1981.
Crawley, P. andDilworth, R. P.,Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs, New Jersey, 1964.
Davey, B.,Subdirectly irreducible distributive double p-algebras, Algebra Universalis8 (1978), 73–88.
Grátzer, G. andLakser, H.,The structure of pseudocomplemented distributive lattices. II: Congruence extension and amalgamation, Trans. Amer. Math. Soc.156 (1971), 343–358.
Jónsson, B.,Universal relational systems, Math. Scand.4 (1956), 193–208.
Jónsson, B.,Sublattices of a free lattice, Canad. J. Math.13 (1961), 256–264.
Jónsson, B.,Extensions of relational structures, inProc. 1963 Int. Symp. at Univ. of Calif., Berkeley, North-Holland, Amsterdam, 1965, pp. 146–157.
Katriňák, T.,Congruence extension property for distributive double p-algebras, Algebra Universalis4 (1974), 273–276.
Katriňák, T.,Infective double Stone algebras, Algebra Universalis4 (1974), 259–267.
Kiss, E. W., Márki, L., Pröhle, P. andTholen, W.,Categorical algebraic properties. Compendium on amalgamation, congruence extension, epimorphisms, residual smallness, and injectivity, Studia Sci. Math. Hungar.18 (1983), 79–141.
Koubek, V. andSichler, J.,Categorical universality of regular double p-algebras, Glasgow Math. J.32 (1990), 329–340.
Pierce, R. S.,Introduction to the Theory of Abstract Algebras, Holt, Rinehart and Winston, New York Montreal London, 1968.
Priestley, H. A.,Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc.2 (1970), 186–190.
Priestley, H. A.,Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc.24 (1972), 507–530.
Priestley, H. A.,Ordered sets and duality for distributive lattices, Ann. Discrete Math.23 (1984), 36–90.
Quackenbush, R.,Structure theory for equational classes generated by quasi-primal algebras, Trans. Amer. Math. Soc.187 (1974), 127–145.
Taylor, W.,Residually small varieties, Algebra Universalis2 (1972), 33–63.
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Dedicated to Bjarni Jónsson on his 70th birthday
The support of the NSERC is gratefully acknowledged by both authors.
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Koubek, V., Sichler, J. Amalgamation in varieties of distributive double p-algebras. Algebra Universalis 32, 407–438 (1994). https://doi.org/10.1007/BF01195722
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DOI: https://doi.org/10.1007/BF01195722