OICC Press Mathematical Analysis and its Contemporary Applications 4 4 2022 09 23 On various properties of module Lau product of algebras 10.30495/maca.2022.1955532.1055 EN Prakash A. Dabhi Department of Mathematics, Institute of Infrastructure Technology Research and Management (IITRAM), Ahmedabad-380026, Gujarat, India Yuvraj D. Pipaliya Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388120, Gujarat, India; General Department, Government Polytechnic, Junagadh-362263, Gujarat, India Journal Article 2022 09 23 Let A, B, and X be complex algebras, θ : B -> X be an algebra homomorphism, and let A be an X-bimodule. We define a product on A × B as (a1, b1)(a2, b2) = (a1a2 + a1 · θ(b2) + θ(b1) ◦ a2, b1b2) for all (a1, b1), (a2, b2) ∈ A × B and write A × B with this product by A ×θ B. We shall study some basic properties of A ×θ B. When A, B and X are Banach algebras, A is a Banach X-bimodule, and θ is a continuous homomorphism with the norm at most 1, we determine the ideals of A ×θ B of a certain type, the Gelfand space of this Banach algebra, and the module multipliers of this Banach algebra.