A version of the Baer splitting problem for noetherian rings

Abstract

A module M over a noetherian ring R is quasi-Baer if Ext_R(M,T) = 0 for each semiartinian module T. We prove that all quasi-Baer modules are projective in case R is commutative with finite Krull dimension.

A non-commutative example of Krull dimension 1 is constructed all of whose modules are quasi-Baer.

Keywords

• version
• splitting
• problem
• noetherian
• rings