Minimal Zero-Dimensional Extensions of Rings of Dimension Greater than One

Abstract

Let R be a commutative ring with Noetherian spectrum in which zero is a primary ideal. We determine the minimal zero-dimensional extensions of R when every regular prime ideal of R is contained in only finitely many prime ideals. This extends previous results of the first author for dim (R) ≤1. We also present a characterization of the partially ordered set of prime ideals in a ring with Noetherian spectrum.

Key Words:

• Noetherian spectrum
• Partially ordered set of prime ideals
• Zero-dimensional extensions

2000 Mathematics Subject Classification:

• 13B02

ACKNOWLEDGMENT

The authors wish to thank Timothy J. Ford for his suggestions and comments. They also thank the referee and the editor for their useful comments.

Notes

Communicated by R. Wiegand.