Geodesic
Characterizations of Modules
Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 608-610

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Fieldhouse, David J. Characterizations of Modules. Canadian journal of mathematics, Tome 23 (1971) no. 4, pp. 608-610. doi: 10.4153/CJM-1971-068-1
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[1] 1. Bass, H., Finitistic hornological dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488. Google Scholar

[2] 2. Bourbaki, N., Algèbre commutative, Chap. I (Hermann, Paris, 1961). Google Scholar

[3] 3. Cohn, P. M., On the free product of associative rings, Math. Z. 71 (1959), 380–398. Google Scholar

[4] 4. Fieldhouse, D., Pure theories, Math. Ann. 184 (1969), 1–18. Google Scholar

[5] 5. Fieldhouse, D., Pure simple and indecomposable rings, Can. Math. Bull. 13 (1970), 71–78. Google Scholar

[6] 6. Lambek, J., Lectures on rings and modules (Blaisdell, Waltham, Mass., 1966). Google Scholar

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