Some remarks on $S$-Noetherian modules

Authors

  • Ajim Uddin Ansari Department of Mathematics, CMP Degree College, University of Allahabad, Prayagraj, India
  • Sanjeev Kumar Maurya Department of Mathematics, Galgotias University, Greator Noida, India
  • B. K. Sharma Department of Mathematics, University of Allahabad, Prayagraj, India

DOI:

https://doi.org/10.3842/umzh.v77i1.7907

Keywords:

Noetherian module, S-Artinian module, S-Noetherian ring, S-Noetherian module, Associated prime ideals

Abstract

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.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 1, 2025.

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Published

25.03.2025

Issue

Vol. 77 No. 1 (2025)

Section

Research articles

License

Copyright (c) 2025 Sanjeev Kumar Maurya MAURYA

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Ansari, Ajim Uddin, et al. “Some Remarks on $S$-Noetherian Modules”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 1, Mar. 2025, p. 72, https://doi.org/10.3842/umzh.v77i1.7907.