Ideals in MV-pairs

Abstract

An MV-pair is a BG-pair (B, G) (where B is a Boolean algebra and G is a subgroup of the automorphism group of B) satisfying certain conditions. Recently, it was proved by Jenča that, given an MV-pair (B, G), the quotient B/~ _G , where ~ _G is an equivalence relation naturally associated with G, is an MV-algebra, and conversely, to every MV-algebra there corresponds an MV-pair. In this paper, we study relations between congruences of B and congruences of B/~ _G induced by a G-invariant ideal I of B. In addition we bring some relations between ideals in MV-algebras and in the corresponding R-generated Boolean algebras.