On Weakly Finite Conductor Rings

Abstract

We define a weakly finite conductor rings with zero divisors, and examine the transfer of these rings to the trivial ring extensions. These results provide examples of a weakly finite conductor rings that are not finite conductor rings (and so not coherent rings). The last section show that the class of weakly finite conductor rings and the class of 2-coherent rings are not comparable.

Key Words:

• Weakly finite conductor properties
• n-presentation
• Trivial extension
• 2-Coherent rings

Acknowledgments

This work was partially supported by the ICTP, Trieste, Italy.

Notes

^#Communicated by S. Wiegand.