Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301The algebra fuzzy norm of the quotient space and pseudo algebra fuzzy normed space35893597613910.22075/ijnaa.2022.6139ENZainab A.KhudhairBranch of Mathematics and Computer Applications, Department of Applied Sciences, University of Technology, Baghdad, IraqJehad RmadhanKiderBranch oh Mathematics and Computer Applications, School of Applied Sciences, University of Technology, Iraq.0000-0002-3173-5654Journal Article20210513The principle aim of this article is to use the notion of algebra fuzzy normed space and its basic properties in order to introduce the notion of algebra fuzzy norm of the quotient space. If the quotient space is fuzzy complete then we prove that U is fuzzy complete. Also, we introduce the notion of pseudo algebra fuzzy normed space and investigate the basic properties of this space. In this direction we define a relation $\sim $ on $ U $ in order to introduce the space $\widehat{{U}}$ of classes $\widehat{ u } =[u]= \{z \in U: z \sim u \} $. If U is pseudo algebra fuzzy normed space then we prove that $\widehat{{U}}$ is algebra fuzzy normed space also if U is a fuzzy complete we prove that $\widehat{{U}}$ is fuzzy complete.https://ijnaa.semnan.ac.ir/article_6139_6a85f59a378a34b454c465b0665ef4b1.pdf