Some Representation Results for (P, Q)-Superlattices
نویسنده
چکیده
On the the lattice (L,∨,∧) we construct the hyperoperations P ∨, Q ∧ as follows: a P ∨ b = a ∨ b ∨ P , a Q ∧ b = a∧ b∧Q. If the sets P,Q ⊆ L satisfy appropriate conditions, then (L, P ∨, Q ∧) is a superlattice. In this paper we give two representation results for (P,Q)-superlattices. The first result is an analog of the [1] representation result. The second result gives necessary and sufficient conditions for a general superlattice to be expressed as a (P,Q)-superlattice; this condition is expressed in terms of associativity of P ∨ with ∨ and of Q ∧ with ∧. AMS Classification Number: 06B99.
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