On almost M-projectives (Q913910)

The concept of almost M-projectives was defined as a generalization of that of M-projectives in 1989 and two papers on properties have been published. In this paper it is shown that the fact that a module \(M_ 0\) is \(M_ i\)-projective for a finite set of modules \(M_ i\) if and only if \(M_ 0\) is \(\sum \oplus M_ i\)-projective, does not translate for almost \(M_ i\)-projectives. Conditions on both the ring and the modules ensure this property to be true and these conditions are examined in the paper. Conditions on the ring include semiperfectness, on the modules \(M_ 0\) locality and on the modules \(M_ i\) certain lifting properties.