On links of certain semiprime ideals of a noetherian ring

TL;DR

This paper establishes a relationship between links of certain semiprime ideals and prime ideals in noetherian rings, showing how automorphism stability influences ideal linkage.

Contribution

It proves that links of { extstyle \sigma}-semistable prime ideals induce links of their largest { extstyle \sigma}-invariant semiprime ideals, and provides a converse result.

Findings

Links of { extstyle \sigma}-semistable prime ideals induce links of their largest { extstyle \sigma}-invariant semiprime ideals.

The paper proves a converse to the main theorem, establishing a bidirectional relationship.

The results deepen understanding of ideal linkage in noetherian rings under automorphisms.

Abstract

In this paper we prove our main theorem, namely, theorem (8), which states that a link Q\rightarrowP, of prime ideals Q and P of a noetherian ring R that are {\sigma}-semistable with respect to a fixed automorphism {\sigma} of R, induces a link Q0\rightarrowP0 of the semiprime ideals Q0 and P0 of the ring R,where Q0 and P0 are the largest {\sigma}- invariant or {\sigma}- stable ideals contained in the prime ideals Q and P. We also prove a converse to this theorem.