Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/3830 2022 2022 Department of mathematics, Latakia University, Latakia, Syria Mohammad Mohammad Department of mathematics, Latakia University, Latakia, Syria Hasan Sankari This paper is dedicated to study 4-cyclic refined vector spaces, where we classify these spaces by using semi-module isomorphisms as direct product of classical complex vector spaces. In addition, we study the inner products defined over these structures and we present sufficient conditions for 4-cyclic refined orthogonality. 2025 2025 01 08 10.54216/GJMSA.0120101 https://www.americaspg.com/articleinfo/33/show/3830