Abstract
Let G be a generalized matrix Banach algebra associated with a Morita context \((A, B, M, N, \Phi , \Psi ).\) In this paper, we investigate biprojectivity and biflatness of G, under certain conditions. Indeed, we obtain a biprojective (resp. biflat) generalized matrix Banach algebra such that \(M\ne 0\) and \(N\ne 0.\) Moreover, we give a sufficient condition for biprojectivity and biflatness of G, in the case where \(A=N=0.\) Using this fact, we obtain some results about homological properties of bi-amalgamated Banach algebras. As an application, we answer some recent open questions.
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Communicated by Saeid Maghsoudi.
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Marzijarani, A.S., Essmaili, M. & Rejali, A. Homological Properties of Some Types of Generalized Matrix Banach Algebras. Bull. Iran. Math. Soc. 48, 3767–3777 (2022). https://doi.org/10.1007/s41980-022-00717-9
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DOI: https://doi.org/10.1007/s41980-022-00717-9