Some remarks on S-Noetherian modules - Ansari, Ajim Uddin; Maurya, Sanjeev Kumar; Sharma, B. K. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 512.5 We study several properties and applications of the S-Noetherian rings and modules. It is proved that an S-Artinian ring is S-Noetherian provided that S contains no zero divisors of the module. Furthermore, it is shown that associated primes exist in modules over the S-Noetherian rings and the major part of notions of associated prime ideals coincide over the S-Noetherian rings. We also extend the classical Krull’s intersection theorem for S-Noetherian rings. Moreover, we provide a characterization of the S-Noetherian modules in terms of the G-graded S-Noetherian modules.