Notes on Intuitionistic Fuzzy Sets Print ISSN 1310–4926, Online ISSN 2367–8283 2024, Volume 30, Number 3, 203-214 DOI: 10.7546/nifs.2024.30.3.203-214 Zariski topology on the spectrum of intuitionistic fuzzy classical primary submodules Poonam Kumar Sharma Post-Graduate Department of Mathematics, D.A.V. College Jalandhar, Punjab, India e-mail: pksharma@davjalandhar.com Received: 7 September 2024 Revised: 8 October 2024 Accepted: 10 October 2024 Online First: 10 October 2024 Abstract: In this paper, we define and study the notion of intuitionistic fuzzy classical primary submodules over a unitary R-module M , where R is a commutative ring with unity. This is a generalisation of intuitionistic fuzzy primary ideals and intuitionistic fuzzy classical prime submodules. We further topologize the collection of all intuitionistic fuzzy submodules on an R-module M with a topology having the intuitionistic fuzzy primary Zariski topology on the intuitionistic fuzzy classical primary spectrum IF cp spec(M ) as a subspace topology and investigate the properties of this topological space. Keywords: Zariski topology, Classical primary submodule, Intuitionistic fuzzy classical primary submodule, Intuitionistic fuzzy classical primary spectrum, Intuitionistic fuzzy primary ideal. 2020 Mathematics Subject Classification: 54C50, 03F55, 16D10, 08A72, 16N80. 1 Introduction Throughout this paper, all rings are commutative with identity, and all modules are unitary. A proper submodule P of an R-module M is called a classical primary submodule if abm ∈ P for a, b ∈ R, and m ∈ M , implies that am ∈ P or b n m ∈ P , for some n ∈ N. The concept of classical primary submodule, which is a generalization of primary ideals and classical prime Copyright © 2024 by the Authors. This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0). https://creativecommons.org/licenses/by/4.0/