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Comptes Rendus de L'Academie Bulgare des Sciences, vol.73, no.12, pp.1650-1657, 2020 (SCI-Expanded)
Let R be a commutative ring and S be a multiplicatively closed subset of R. A proper ideal P of R is called locally S-prime if PSis a prime ideal of RS. It is shown that, P is a locally S-prime ideal if and only if whenever P ∩ S = Ø and if ab ∈ P for some a; b ∈ R, then there exists s ∈ S such that sa ∈ P or sb ∈ 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.