Karya
Judul/Title The Relation between Almost Noetherian Module, Almost Finitely Generated Module and T-Noetherian Module
Penulis/Author AHMAD FAISOL (1) ; Dr. Budi Surodjo, M.Si. (2); Prof. Dr. Sri Wahyuni, S.U. (3)
Tanggal/Date 8 2019
Kata Kunci/Keyword
Abstrak/Abstract In this paper we study the relation between almost Noetherian modules, almost nitely generated (a.f.g.) modules, and T-Noetherian modules. We show that if R0 = fr 2 RjrM 6= Mg and M is an almost Noetherian (a.f.g. resp.) R-module, then M is an (R0)- Noetherian module. We also obtain that for any multiplicatively closed subset T of a ring R and R0 = fr 2 RjrM 6= Mg, if M is an almost Noetherian (a.f.g. resp.) R-module and T \ R0 6= ;, then M is (T \ R0)-Noetherian. Moreover, we show that if M is an almost Noetherian (a.f.g. resp.) R-module and T \ R0 6= ;, then M is an T-Noetherian module for every multiplicatively closed set T R. Finally, we apply the results of this paper on the structure of Generalized Power Series Module (GPSM) M[[S]].
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