Equational Classes of Distributive Pseudo-Complemented Lattices
1970 ◽
Vol 22
(4)
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pp. 881-891
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A pseudo-complemented lattice is a lattice L with zero such that for every a ∊ L there exists a* ∊ L such that, for all x ∊ L, a ∧ x = 0 if and only if x ≦ a*. a* is called a pseudo-complement of a. It is clear that for each element a of a pseudo-complemented lattice L, a* is uniquely determined by a. Thus * can be regarded as a unary operation on L. Moreover, each pseudo-complemented lattice contains the unit, namely 0*. It follows that every pseudo-complemented lattice L can be regarded as an algebra (L; (∧, ∨, *, 0, 1)) of type (2, 2, 1, 0, 0). In this paper, we consider only distributive pseudo-complemented lattices. For simplicity, we call such a lattice a p-algebra.
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2004 ◽
Vol 47
(2)
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pp. 191-205
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1988 ◽
Vol 30
(2)
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pp. 137-143
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1989 ◽
Vol 31
(1)
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pp. 1-16
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2000 ◽
Vol 248
(6)
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pp. 492-500
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2017 ◽
Vol 201
(7-9)
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pp. 1209-1225
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2015 ◽
Vol 199
(7)
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pp. 1211-1213
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