Almost maximal prüfer domains

Abstract

A well-known theorem of Brandal states that if R is an almost maximal Prüifer domain with quotient field Q, then every homomorphic image of Q is injective. The converse of Brandal's theorem is established, and it is shown in addition that a Prüfer domain is almost maximal if and only if each prime ideal has injective dimension one. Applications involving reflexive domains are considered.

Keywords:

• Prüfer domain
• almost maximal ring
• injective module

1991 Mathematics Subject Classification:

• Primary: 13F05
• Primary: 13C11
• Secondary: 18G05
• Secondary: 16D50