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Jun 1, 2013 · Suppose A = 〈 A, ≤ t, ≤ f, ≤ i, − t, − f, − i 〉 is an interlaced trilattice with t-, f- and i-involutions. Notice that neither − f nor − i is compatible with ∼ 1 (nor with ∼ 2), but it is easy to prove that the composition of the two operation is. Proposition 3.8. Let A be an interlaced trilattice with t-, f- and i ...
- Umberto Rivieccio
- 2013
Jun 1, 2013 · The property of interlacing-which appears frequently in the theory of bilattices as well-is a very natural property, being exhibited by the most common bilattices and trilattices (e.g., F OUR 2 , N...
- Umberto Rivieccio
Both consist of repeating layers of hexagonally arranged atoms. In both types, a second layer (B) is placed on the first layer (A) so that each atom in the second layer is in contact with three atoms in the first layer. The third layer is positioned in one of two ways.
A pre-bilattice is called interlaced [7] when all four lattice operations are monotone w.r.t. to both lattice orders. It is called distributive [12] when all possible distributive laws concerning the four lattice operations, i.e., any identity of the following form, hold:
Algebraically, trilattices can be characterized by nine types of trilattice equations. Apart from the idempotent, associative, and commutative laws, further types of identities are needed such as bounds and limits laws, antiordinal, absorption, and separation laws.
- Klaus Biedermann
- 1999
Jul 15, 2022 · As is shown in the figures above, although especially in the right one, any lattice that describes the repetition of the motif (triangle + circle) can be decomposed into two identical equivalent lattices (one for each object of the motif). Thus, the concept of lattice is independent of the complexity of the motif, so that we can use only one ...
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The main results are that every interlaced bilattice is isomorphic to the Ginsberg-Fitting product of two bounded lattices and that the variety of interlaces bilattices is equivalent to the varieties of bounded lattice with two distinguishable distributive elements, which are complements of each other.
