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Relative Ockham lattices: Their order-theoretic and algebraic characterisation. (English) Zbl 0693.06009
Given a variety A of lattice-ordered algebras, a lattice L is said to be a relative A-algebra if every closed interval of L can be given the structure of an algebra in A. The class of lattice-ordered algebras under consideration here is the class of Ockham algebras (bounded distributive lattices together with a dual endomorphism). If A, B are varieties of Ockham algebras define \(A\approx B\) if and only if the class of finite relative A-algebras coincides with the class of finite relative B- algebras. This is an equivalence relation on the varieties of Ockham algebras, and the main objective of the paper is to describe the equivalence classes of the varieties of Boolean, de Morgan, and Stone algebras. Varieties of distributive p-algebras are also considered.
Reviewer: T.S.Blyth

MSC:
06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
06B20 Varieties of lattices
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References:
[1] Davey, Ordered sets pp 43– (1982) · doi:10.1007/978-94-009-7798-3_2
[2] Davey, Colloq. Math. Soc. Jdnos Bolyai 33 pp 101– (1983)
[3] DOI: 10.1007/BF02485743 · Zbl 0299.06007 · doi:10.1007/BF02485743
[4] DOI: 10.2307/2040604 · Zbl 0294.06008 · doi:10.2307/2040604
[5] DOI: 10.1016/0012-365X(83)90256-X · Zbl 0521.06014 · doi:10.1016/0012-365X(83)90256-X
[6] DOI: 10.1007/BF00401657 · Zbl 0511.06007 · doi:10.1007/BF00401657
[7] DOI: 10.1007/BF00370442 · Zbl 0425.06008 · doi:10.1007/BF00370442
[8] Rival, Contemporary Math. 57 pp 263– (1986) · doi:10.1090/conm/057/856239
[9] Ramalho, Port. Math. 44 pp 315– (1987)
[10] Blyth, Bull. Roy. Soc. Liège 54 pp 167– (1985)
[11] Blyth, Proc. Roy. Soc. Edinburgh Sect. A 95 pp 157– (1983) · Zbl 0544.06011 · doi:10.1017/S0308210500015869
[12] Blyth, Proc. Roy. Soc. Edinburgh Sect. A 94 pp 301– (1983) · Zbl 0536.06013 · doi:10.1017/S0308210500015663
[13] DOI: 10.1016/0021-8693(88)90248-7 · Zbl 0671.06007 · doi:10.1016/0021-8693(88)90248-7
[14] DOI: 10.1016/S0012-365X(81)80027-1 · Zbl 0468.06004 · doi:10.1016/S0012-365X(81)80027-1
[15] DOI: 10.1007/BF01836429 · Zbl 0395.06007 · doi:10.1007/BF01836429
[16] Balbes, Distributive lattices (1974)
[17] Priestley, Ann. Discrete Math. 23 pp 39– (1984)
[18] Jónsson, Math. Scand. 21 pp 110– (1967) · Zbl 0167.28401 · doi:10.7146/math.scand.a-10850
[19] DOI: 10.1016/0012-365X(87)90006-9 · Zbl 0608.06004 · doi:10.1016/0012-365X(87)90006-9
[20] Goldberg, Bull. Austral. Math. Soc. 24 pp 161– (1981)
[21] Davey, Houston J. Math. 5 pp 183– (1979)
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