Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6449 2771-6430 10.54216/JNFS https://www.americaspg.com/journals/show/1009 2021 2021 Gaziantep University, Turkey Mikail Bal Department of Computer science and Engineering, Gandhi institute of Technology and Management-Visakhapatnam 530045, India Prem Kumar Singh Islamic university Of Gaza, Palestine Katy D. Ahmad Recently, Turiyam set is introduced for dealing the fourth dimensional data sets. These types of data sets exists when an expert unable to categorize them in Euclidean, Non-Euclidean, Hybrid or NeutroGeometry. To deal with these types of data set Turiyam matrix and its algebra is required. Hence the current paper introduce the concept of Symbolic Turiyam R-module as a generalization of the corresponding neutrosophic one by using the algebra of symbolic Turiyam set. The paper also presents concept pf finite Turiyam modulo integer and illustrate many examples to show and clarify the validity of this work. 2022 2022 8 19 10.54216/JNFS.020201 https://www.americaspg.com/articleinfo/24/show/1009