Biﬂatness of Banach algebras modulo an ideal

Abolfathi, Mohammad Ali; Mewomo, Oluwatosin Temitope

doi:10.30495/maca.2021.1932071.1013

Biﬂatness of Banach algebras modulo an ideal

https://doi.org/10.30495/maca.2021.1932071.1013

Volume 3, Issue 2
Spring 2021

Pages 68-74

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Mohammad Ali Abolfathi ¹

Oluwatosin Temitope Mewomo ²

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

Keywords

Amenability

amenability modulo an ideal

biﬂatness modulo an ideal

biprojectivity modulo and ideal