SOME PROPERTIES AND THE DISTRIBUTIVITY OF THE (P, Q)-SUPERLATTICE
K. Serafimidis, Maria Konstantinidou · 2004
We consider 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 explore some properties of (L, P ∨, Q ∧) with special attention to various types of P ∨ and Q ∧ distributivity. AMS Subject Classification: 06B99, 06D99.