Some Results on Injective Modules Over a Ring of Krull Type

ABSTRACT

In this article, we study injective modules over a ring of Krull type A. Our main result is E(K/A)≃ ⨁_{ω∈Ω ^t} E(K/ℜ_ω), where Ω ^t is a thin defining family of valuations of A. We also characterize the rings of Krull type A such that TE(K/A) is a cogenerator of the quotient category Mod(A)/ℳ₀, where ℳ₀ is the thick subcategory of the modules with trivial maps into the codivisorial modules.

Key Words:

• Codivisorial
• Injective module
• Valuation-ring of Krull type

1991 Mathematics Subject Classification:

• 13C

ACKNOWLEDGMENT

The author would like to thank the referee who suggested some improvements of the manuscript.

Notes

Communicated by I. Swanson.