Essential Ideals in Rings of Measurable Functions

Abstract

In this article, we study essential ideals, socle, and some related ideals of rings of real valued measurable functions. We also study the Goldie dimension of rings of measurable functions.

Key Words:

• Goldie dimension
• Rings of continuous functions
• Rings of measurable functions
• ℵ₀-Self-injective regular rings and ℵ₀-continuous regular rings

2000 Mathematics Subject Classification:

• Primary 54C40
• Secondary 13A30

ACKNOWLEDGMENT

The author would like to thank the referee for his/her careful reading and many helpful comments on the article.

Notes

Communicated by T. Albu.

Dedicated to the memory of Professor Melvin Henriksen.