Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 10.54216/PAMDA https://www.americaspg.com/journals/show/3495 2022 2022 Department of Mathematics; Faculty of Education and Sciences; Saba Region University; Yemen Shawqi Shawqi Faculty of Education, Humanities and Applied Sciences (Khawlan), Yemen; and Department of Foundations of Sciences, Faculty of Engineering, Sana'a University. Box:13509, Sana'a, Yemen Adel Al Al-Odhari The main objective of this paper is to present a review study with more information on the neutrosophic Ideal, Principle Ideal, Prim Ideal, Pseudo Neutrosophic Ideal, Quotient ring, and Pseudo Quotient ring. Neutrosophic ring theory is a branch of neutrosophic Algebra which introduced by Florentin Smarandache in 2006. 2024 2024 01 13 10.54216/PAMDA.040101 https://www.americaspg.com/articleinfo/34/show/3495