Abstract
A right R-module M is called a D3-module, if M
1
and M
2
are direct summands of M with M = M
1
+ M
2
, then M
1
∩ M
2
is a direct summand of M. Following the work of Bass on projective covers, we introduce the notion of D3-covers and provide new characterizations of several well-known classes of rings in terms of D3-modules and D3-covers.