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Jun 1, 2013 · Let A = 〈 A, ≤ t, ≤ f, ≤ i, − t 〉 be an interlaced trilattice with t-involution. Using De Morgan laws, it is not difficult to prove the following: Proposition 3.5. The relations ∼ 1 and ∼ 2 defined in the previous section are congruences of any interlaced trilattice with t-involution. Proof
- Umberto Rivieccio
- 2013
Figure 10.6.3 10.6. 3: An atom in a simple cubic lattice structure contacts six other atoms, so it has a coordination number of six. In a simple cubic lattice, the unit cell that repeats in all directions is a cube defined by the centers of eight atoms, as shown in Figure 10.6.4 10.6. 4.
Jun 1, 2013 · In [31], Rivieccio presented product representations for the varieties of interlaced trilattices and interlaced trilattices with one involution´t. A trilattice is said to be interlaced if the six ...
- Umberto Rivieccio
distributive, while the seven-element one is not (in fact, it is not even interlaced). The diagrams should be read as follows: a b if there is a path from a to b which goes uniformly from left to right, while a b if there is a path from a to b
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.
This paper presents the new algebra of trilattices, which are understood as the triadic generalization of lattices. As with lattices, there is an order-theoretic and an algebraic approach to trilattices. Order-theoretically, a trilattice is defined as a triordered set in which six triadic operations of some small arity exist. The Reduction Theorem guarantees that then also all finitary ...
Dec 1, 1999 · Abstract. This paper presents the new algebra of trilattices, which are understood as the triadic generalization of lattices. As with lattices, there is an order-theoretic and an algebraic approach to trilattices. Order-theoretically, a trilattice is defined as a triordered set in which six triadic operations of some small arity exist. The Reduction Theorem guarantees that then also all ...
