Isomorphisms of semirings of continuous nonnegative functions with max-addition and isomorphisms of lattices of their subalgebras

摘要

Let R ∨ be the semifield with zero of nonnegative real numbers with operations of max-addition and multiplication and C ∨ (X) be the semiring of continuous R ∨ -valued functions on an arbitrary topological space X with pointwise operation max-addition and multiplication. We call a subset A ? C ∨ (X) a subalgebra of the semiring C ∨ (X) if f ∨ g, fg, rf ∈ A for any f, g ∈ A and r ∈ R ∨ . For arbitrary topological spaces X and Y, we describe isomorphisms of the lattices of subalgebras (subalgebras with unity) of the semirings C ∨ (X) and C ∨ (Y ).