Homological Properties of Some Types of Generalized Matrix Banach Algebras

Let G be a generalized matrix Banach algebra associated with a Morita context ( A , B , M , N , Φ , Ψ ) . 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 ≠ 0 an...

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Bibliographic Details
Published in:	Bulletin of the Iranian Mathematical Society Vol. 48; no. 6; pp. 3767 - 3777
Main Authors:	Marzijarani, Azam Salehi, Essmaili, Morteza, Rejali, Ali
Format:	Journal Article
Language:	English
Published:	Singapore Springer Nature Singapore 01-12-2022
Subjects:	Mathematics Mathematics and Statistics Original Paper Biflatness Bi-amalgamated Banach algebras 43A20 Biprojectivity 15A78 46M10 Generalized matrix Banach algebras
Online Access:	Get full text
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Summary:	Let G be a generalized matrix Banach algebra associated with a Morita context ( A , B , M , N , Φ , Ψ ) . 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 ≠ 0 and N ≠ 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.
ISSN:	1017-060X 1735-8515
DOI:	10.1007/s41980-022-00717-9