Hilbert basis theorem for generalized Noetherian rings

Authors

  • Xiaolei Zhang School of Mathematics and Statistics, Tianshui Normal University, Tianshui, China

DOI:

https://doi.org/10.3842/umzh.v78i5-6.9329

Keywords:

Hilbert Basis Theorem, uniformly S-Noetherian ring, S-w-Noetherian ring

Abstract

UDC 512.552

We explore the Hilbert Basis Theorem for uniformly $S$-Noetherian rings, $S$-$w$-Noetherian rings, and uniformly $S$-$w$-Noetherian rings. Moreover, we also show that uniformly $S$-($w$-)Noetherian rings may be not ($w$-)Noetherian even in the case where $S$ consists of nonzero divisors.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 5-6, 2026.

Downloads

Published

29.05.2026

Issue

Vol. 78 No. 5-6 (2026)

Section

Research articles