Arabaci, TarikSevim, Esra Sengelen2024-07-182024-07-1820201310-1331https://doi.org/10.7546/CRABS.2020.12.03https://hdl.handle.net/11411/8245Let R be a commutative ring and S be a multiplicatively closed subset of R. Lambda proper ideal P of R is called locally S-prime if P-S is a prime ideal of R-S. It is shown that, P is a locally S-prime ideal if and only if whenever P boolean AND S = ? and if ab is an element of P for some a, b is an element of R, then there exists s is an element of S such that sa is an element of P or sb is an element of P. As a consequence of this fact and well-known properties of prime ideals we obtain some properties of these ideals. Also, all multiplicatively closed subsets S of R that an ideal can be locally S-prime are characterised. Finally, these ideals are studied in an S-Noetherian ring.eninfo:eu-repo/semantics/closedAccessLocally S-Prime İdealS-Noetherian RingArticle2-s2.0-8509975716410.7546/CRABS.2020.12.03165712Q3165073Q4WOS:000608240800003