1982
DOI: 10.1017/s0013091500016710
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α-Representable coproducts of distributive lattices

Abstract: There are a number of classes of distributive lattices whose members can be characterised as the coproduct A In this note we investigate the a-representability of the coproduct A * L of two distributive lattices. In Section 2 we show (Theorem 2.3) that if L is finite, then A * L is a-complete if and only if A is a-complete, and (Theorem 2.6) if L is arbitrary and B is a Boolean algebra, then B * L is a-complete if and only if both B and L are a-complete and at least one of them is finite. The a-representabilit… Show more

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“…In this note we show that both (DO and (Dz) hold for a Post L-algebra P= (B, L) with a finite lattice of constants L. Post L-algebras were introduced by T. P. Speed in [2] and further investigated by the author in [3] and [4]. It is shown in [2] that if L is a bounded distributive lattice, then every Post L-algebra P is isomorphic to the coproduct of a Boolean algebra B and L, where the coproduct is taken in the category of bounded distributive lattices and lattice homomorphisms preserving 0 and 1.…”
Section: A Theorem On Infinite Distributivity For Post L-algebrasmentioning
confidence: 91%
“…In this note we show that both (DO and (Dz) hold for a Post L-algebra P= (B, L) with a finite lattice of constants L. Post L-algebras were introduced by T. P. Speed in [2] and further investigated by the author in [3] and [4]. It is shown in [2] that if L is a bounded distributive lattice, then every Post L-algebra P is isomorphic to the coproduct of a Boolean algebra B and L, where the coproduct is taken in the category of bounded distributive lattices and lattice homomorphisms preserving 0 and 1.…”
Section: A Theorem On Infinite Distributivity For Post L-algebrasmentioning
confidence: 91%