S-Prime Ideals in Principal Domain

Mohamed Aqalmoun (Department of Mathematics, Higher Normal School, Sidi Mohamed Ben Abdellah University, Fez)

Journal of the Indonesian Mathematical Society
VOLUME 29 NUMBER 1 (MARCH 2023)

Let R be a commutative ring and S be a multiplicative subset of R. The S-prime ideal is a generalization of the concept of prime ideal. In this paper, we completely determine all S-prime and S-maximal idealsof a principal domain. It is shown that the intersection of any descending chain of S-prime ideals in a principal domain is an S-prime ideal, also the S-radical is investigated.