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Let A and B be Banach algebras with preduals A∗ and B∗ respectively, and
Θ : B → A be an algebraic homomorphism. In this paper, we derive some specific results
concerning the characterizations of module Connes amenability of certain Banach algebras.
Indeed, we investigate and give necessary and sufficient conditions for module Connes
amenability of projective tensor product Ab⊗B. Moreover, we characterize the module (ψ, θ)-
Connes amenability of Θ-Lau product A×Θ B, which ψ and θ are homomorphisms in A∗ and
B∗, respectively.