We show that there are a cardinal μ, a σ-ideal I ⊆ P(μ) and a σ-subalgebra B of subsets of μ extending I such that B/I satisfies the c.c.c. but the quotient algebra B/I has no lifting. 0. Introduction. In the present paper we prove the following theorem. Theorem 0.1. For some μ (in fact, μ = (2א0)++ suffices) there is a σ-ideal I on P(μ) and a σ-subalgebra B of P(μ) extending I such that B/I sa...