Published online by Cambridge University Press: 20 November 2018
In this paper we use the Bourbaki [2] conventions for rings and modules. All rings are associative but not necessarily commutative and have a 1; all modules are unital.
Bass [1] calls a ring A left perfect if and only if every left A -module has a projective cover, which he shows is equivalent to every flat left A -module being projective. Bass calls a ring A semi-perfect if and only if every finitely generated module has a projective cover and shows that this concept is leftright symmetric.
We will define a ring A to be quasi-perfect if and only if every finitely generated flat left A -module is projective.
An exercise [6, Exercise 10, p. 136] is given by Lambek to show that every semi-perfect ring is quasi-perfect.