Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 6 3 2025 07 01 Left ϕ-biflatness and ϕ-biprojectivity of certain Banach algebras with applications 279 287 5384 10.22060/ajmc.2024.22985.1211 EN Solaleh Salimi Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran Amin Mahmoodi Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran Mehdi Rostami Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran Amir Sahami Department of Mathematics Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran Journal Article 2024 02 08 This paper continues the investigation initially begun in [24]. We show that left ϕ-biflatness and left ϕ-biprojectivity are closely related to the notions of left ϕ-amenability and ϕ-inner amenability. We characterize left ϕ-biprojectivity and left ϕ-biflatness of certain semigroup algebras and some algebras related to a locally compact group. We discuss non left ϕ-biflatness of some specified triangular Banach algebras. https://ajmc.aut.ac.ir/article_5384_ccda9caac31224cf184c3e0b5868b1b7.pdf