The Sufficient Conditions for R[X]-module M[X] to be S[X]-Noetherian

  • Ahmad Faisol Universitas Gadjah Mada
  • Budi Surodjo Universitas Gadjah Mada
  • Sri Wahyuni Universitas Gadjah Mada
Keywords: $S$-Noetherian module, Polynomial module, Laurent polynomial module, Power series module, Laurent series module

Abstract

In this paper, we obtain the necessary and sufficient conditions on a ring $R$, a multiplicative set $S\subseteq R$, and an $R$-module $M$ such that the polynomial module, the Laurent polynomial module, the power series module, and the Laurent series module are $S$-Noetherian. Furthermore, we also obtain the sufficient conditions for these modules to be $S[X]$-Noetherian, $S[X,X^{-1}]$-Noetherian, $S[[X]]$-Noetherian, and $S[[X,X^{-1}]]$-Noetherian, respectively.

Published
2019-01-23
How to Cite
Faisol, A., Surodjo, B., & Wahyuni, S. (2019). The Sufficient Conditions for R[X]-module M[X] to be S[X]-Noetherian. European Journal of Mathematical Sciences, 5(1), 1-13. Retrieved from http://www.ejmathsci.org/index.php/ejmathsci/article/view/245
Section
Articles