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 inBulletin of the Iranian Mathematical Society Vol. 48; no. 6; pp. 3767 - 3777
Main Authors Marzijarani, Azam Salehi, Essmaili, Morteza, Rejali, Ali
Format Journal Article
LanguageEnglish
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
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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