The Structure of the (P, Q)-Superlattice and Order Related Properties
نویسندگان
چکیده
In a previous work we have introduced the (P,Q)-superlattice, a hyperstructure of the form (L, P ∨, Q ∧). Here (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined by a P ∨b . = a∨b∨P , a Q ∧b . = a∧b∧Q; when the sets P,Q ⊆ L satisfy appropriate conditions (L, P ∨, Q ∧) is a superlattice. In this work we continue the investigation of (P,Q)superlattice and consider the structure of the sets a P ∨ b, a Q ∧ b as well assome “order-like” relationships between such sets. AMS classification number: 06B99.
منابع مشابه
An Investigation of the Properties of the (p, Q)-superlattice
The (P,Q)-superlattice is a hyperstructure of the form (L, P ∨, Q ∧), where (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined 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. We examine the properties of the sets a P ∨ b and a Q ∧ b in connection to the properties of P,Q. Especial...
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