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Zbl 0571.16015
Hausen, Jutta; Johnson, Johnny A.
On the existence of projective and quasi-projective covers. (English)
[J] Rend. Sem. Mat. Univ. Padova 73, 49-54 (1985). ISSN 0041-8994

The authors prove the following results: A ring R (associative, with identity) is semi-perfect iff every 2-generated module has a quasi- projective cover, iff every 1-generated quasi-projective module is quasi- perfect, iff every 1-generated module has a quasi-perfect cover (Th.1.2). A ring R is semisimple artinian iff every 2-generated module is quasi- projective.
[L.Bican]

MSC 2000:: *16L30 Noncommutative local and semilocal rings
16D40 Free, etc. modules and ideals (assoc. rings and algebras)
16Kxx Division rings and semi-simple Artin rings

Keywords: 2-generated module; quasi-projective cover; quasi-projective module; quasi-perfect; quasi-perfect cover; semisimple artinian

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