Abstract
In a pseudocomplemented de Morgan algebra, it is shown that the set of kernel ideals is a complete Heyting lattice, and a necessary and sufficient condition that the set of kernel ideals is boolean (resp. Stone) is derived. In particular, a characterization of a de Morgan Heyting algebra whose congruence lattice is boolean (resp. Stone) is given.
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References
Beazer, R.: Lattices whose ideal lattice is Stone. Proc. Edin. Math. Soc. 26, 107–112 (1983)
Blyth, T.S., Varlet, J.C.: Ockham Algebras. Oxford University Press, Oxford (1994)
Blyth, T.S.: Lattices and Ordered Algebraic Structures. Springer-Verlag, London (2005)
Castaño, V., Santis, M.M.: Subalgebras of Heyting and de Morgan Heyting algebras. Studia Logica. 98, 123–139 (2011)
Castaño, V., Santis, M. M.: De Morgan Heyting algebras satisfying the identity x n(∘∗) = x (n+1)(∘∗). Math. Log. Quart. 57(3), 236–245 (2011)
Chajda, I., Halas, R., Kuhr, J.: Semilattice structures. Heldermann Verlag (2007)
Cornish, W.H.: Congruences on distributive pseudocomplemented lattices. Bull. Austral. Math. Soc. 8, 161–179 (1973)
Grätzer, G.: General Lattice Theory. Birkhäsuer-Verlag, Basel (1978)
Monteire, A.: Sur les Algèbres de Heyting Symétriques. Portugaliae Math. 31, 1–237 (1980)
Nimbhorkar, S.K., Rahemani, A.: A note on Stone join-semilattices. Cent. Eur. J. Math. 9(4), 929–933 (2011)
Romanowska, A.: Subdirectly irredubible pseudocomplemented de Morgan algebras. Algebra Universalis 12, 70–75 (1981)
Sankappanavar, H.P.: Principal congruences of pseudocomplemented de Morgan algebras. Zeitchr. f. math. Logik und Grundlagen d Math. 33, 3–11 (1987)
Sankappanavar, H.P.: Heyting algebras with a dual lattice endomorphism. Zeitchr. f. math. Logik und Grundlagen d Math. 33, 565–573 (1987)
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Wang, XP., Wang, LB. The Lattices of Kernel Ideals in Pseudocomplemented De Morgan Algebras. Order 34, 23–35 (2017). https://doi.org/10.1007/s11083-016-9386-z
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DOI: https://doi.org/10.1007/s11083-016-9386-z