On various properties of module Lau product of algebras
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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JR_MACA-4-4_001
تاریخ نمایه سازی: 6 شهریور 1402
Abstract:
Let \mathcal{A}, \mathcal{B}, and \mathcal{X} be complex algebras, \theta : \mathcal{B} \longrightarrow \mathcal{X} be an algebra homomorphism, and let \mathcal{A} be an \mathcal{X}-bimodule. We define a product on \mathcal{A} \times \mathcal{B} as (a_۱, b_۱)(a_۲,b_۲) = (a_۱ a_۲ + a_۱ \cdot \theta(b_۲) + \theta(b_۱) \circ a_۲,b_۱ b_۲) for all (a_۱, b_۱), (a_۲,b_۲) \in \mathcal{A} \times \mathcal{B} and write \mathcal{A} \times \mathcal{B} with this product by \mathcal{A} \times_\theta\mathcal{B}. We shall study some basic properties of \mathcal{A} \times_\theta \mathcal{B}. When \mathcal{A}, \mathcal{B} and \mathcal{X} are Banach algebras, \mathcal{A} is a Banach \mathcal{X}-bimodule, and \theta is a continuous homomorphism with the norm at most ۱, we determine the ideals of \mathcal{A} \times_\theta \mathcal{B} of a certain type, the Gelfand space of this Banach algebra, and the module multipliers of this Banach algebra.
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Authors
Prakash Dabhi
Department of Mathematics, Institute of Infrastructure Technology Research and Management (IITRAM), Ahmedabad - ۳۸۰۰۲۶, Gujarat, India
Yuvraj Pipaliya
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar- ۳۸۸۱۲۰, Gujarat, India