Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495220240401Approximate left $\varphi$-biprojectivity of $\theta$-Lau product algebras111116489610.22060/ajmc.2022.21637.1093ENSalmanBabayiDepartment of Mathematics, Faculty of Sciences, Urmia University, Urmia, IranMehdiRostamiDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran0000-0002-8989-0286MonaAjDepartment of Mathematics, Farhangian University of Kermanshah, Kermanshah, IranAmirSahamiDepartment of Mathematics, Faculty of Basic Sciences Ilam University P.O. Box 69315-516 Ilam, Iran0000-0003-0041-509XJournal Article20220728We continue [8] and we discuss approximately left $\phi$-biprojectivity for $\theta$-Lau product algebras. We give some Banach algebras among the category of $\theta$-Lau product algebras which are not approximately left $\phi$-biprojective. In fact, some class of matrix algebras under the notion of approximate left $\phi$-biprojectivity is also discussed here.https://ajmc.aut.ac.ir/article_4896_ce78285638338b3b98f8fa3a6af3a954.pdf