aspg-34-3495-1791485083 20261008184443 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 2024 4 1 Shawqi Al-lkami Department of Mathematics; Faculty of Education and Sciences; Saba Region University; Yemen Adel Al-odhari 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 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 01 08 3495 https://creativecommons.org/licenses/by/4.0/ 10.54216/PAMDA.040101 https://www.americaspg.com/journal/34/article/3495 https://www.americaspg.com/storage/articles/manuscripts/01M1MTYRXVBJ4P9155802FYWMD.pdf