Some Homological Properties of Subring Retract and Applications to Fixed Rings

Abstract

In this paper we study the relationship between some homological properties such as the weak and the global dimension, the strong n-coherence, and the (n, d)-property, where n and d are two integers, of a commutative ring and its subrings retract. A special application is the transfer of these properties from a commutative ring to its fixed subring with respect to a subgroup of its group of automorphisms. It concludes with a discussion of the scopes and limits of our results.

Key Words:

• n-presentation
• Strong n-coherence
• (n, d)-property
• Subring retract
• Fixed subring

Notes

^#Communicated by S. Wiegand.