Isomorphisms of lattices of subalgebras of the semifield of continuous positive functions with max-addition
В. В. Сидоров · Sibirskie Elektronnye Matematicheskie Izvestiya · 2019
Let P ∨ be the semifield of positive real numbers with operations of max-addition and multiplication and U ∨ (X) be the semifield of continuous P ∨ -valued functions on an arbitrary topological space X with pointwise operation max-addition and multiplication.We call a subset A ⊆ U ∨ (X) a subalgebra if f ∨ g, f g, rf ∈ A for any f, g ∈ A, r ∈ P ∨ .We describe isomorphisms of lattices of subalgebras of semifields U ∨ (X).