March 3, 2026

Lasker–Noether Theorem for Nonnil- S -Noetherian Rings

Key Points

The Lasker–Noether theorem is thereby extended to nonnil-S-Noetherian rings, enabling broader applications in algebra.
We show that any ring allowing an S-primary decomposition also allows a minimal S-primary decomposition.
Using S-primary decomposition, we establish the S-version of Krull’s intersection theorem within S-Noetherian domains.
This extension may provide new insights and tools for tackling problems related to ring theory less constrained than traditional frameworks.

Abstract

We introduce the concept of S -primary decomposition for a commutative ring and show that if a ring admits an S -primary decomposition, then it admits a minimal S -primary decomposition. We establish the S -version of Krull’s intersection theorem by using the existence of S -primary decomposition in S -Noetherian domains. As the main result, we prove the Lasker–Noether theorem for nonnil- S -Noetherian rings, thereby extending the classical Lasker–Noether theorem.

Bookmark

Cite This Study

Singh et al. (Thu,) studied this question.

synapsesocial.com/papers/69a75d75c6e9836116a27885 https://doi.org/https://doi.org/10.1134/s0037446626010222

Bookmark