TY - JOUR T1 - Biflatness of Abstract Segal Algebras Based on Characters TT - دوتختی بودن جبرهای سگال مجرد بر پایۀ مشخصه‌ها JF - khu-mmr JO - khu-mmr VL - 7 IS - 1 UR - http://mmr.khu.ac.ir/article-1-3056-en.html Y1 - 2021 SP - 101 EP - 110 KW -  Abstract KW -  Segal algebra KW - left 𝜙-biflat KW - left 𝜙-amenable KW - inner 𝜙-amenable 2010 Mathematics Subject Classification: 64M10 KW - 43A07 KW - 43A20.  N2 - In this paper, we investigate and study the notion of left -biflatness of abstract Segal algebras, where is a character on Banach algebra. Precisely, we give a necessary and sufficient condition for left -biflatness of abstract Segal algebras equipped with a left approximate identity. As an application, we show that if is a Segal algebra on the locally group and is a character, then is left -biflat if and only if is amenable. Indeed, this is a generalization of [4, Theorem 3.4]. Moreover, we study the relationship between left -biflatness and inner -amenability and show that if the Banach algebra is inner -amenable, then the notions of left -biflatness and left -amenability are equivalent../files/site1/files/71/10.pdf M3 10.52547/mmr.7.1.101 ER -