Research Information System
Ukrainian Mathematical Journal, vol.77, no.10, pp.1375-1387, 2025 (SCI-Expanded, Scopus)
We study S-prime hyperideals by relating them to prime hyperideals. The S-prime hyperideals are studied in the hyperfield of fractions in the Krasner hyperring. The characterization of S-prime hyperideals is determined under a strong homomorphism. With the help of strong epimorphisms, the conditions for one-to-one correspondence between the S-prime hyperideals in the hyperring and S-prime hyperideals in the hyperfield of fractions of these hyperrings are investigated. The concept of S-prime subhypermodules of Krasner hypermodules is introduced. In particular, the S-spectrum SpecS of the S-Zariski topology is obtained, which is based on the element of S-prime subhypermodules of a class of these hypermodules. Moreover, characterizations of S-prime subhypermodules are given in the perspective of the S-spectrum.