Document Type : Original Article
Authors
1 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran
2 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
Abstract
Biflatness of Banach algebras is one of the important topics in the study of cohomological properties of Banach algebras. This concept has a close relationship with the amenability of Banach algebras. In this paper, we introduce a new notion namely biflatness of Banach algebras modulo closed ideals. Moreover, we define the concept of virtual diagonal modulo ideals for investigating biflatness of Banach algebras modulo closed ideals. We show that biflatness of a Banach algebra A modulo I is equivalent to the existence of I -virtual diagonal modulo ideal I. By this result, we show that amenability of A/I implies biflatness of A modulo I. Moreover, we investigate the relationship of biflatness of the Banach algebra A modulo I with the biflatness of A/I . Finally, biflatness of Banach algebras modulo closed ideals is weaker than biprojectivity of them modulo closed ideals and provide examples to better understand the content
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