When every projective module is a direct sum of finitely generated modules. (English) Zbl 1126.13008
The authors investigate the question of when every projective right module is a direct sum of finitely generated modules. The main result is a precise criterion for every projective right module having the aforementioned property. Using this criterion they give a new proof of a Bergman’s result that ensures that every projective module over a weakly semihereditary ring is a direct sum of finitely generated modules.
Reviewer: Marco Fontana (Roma)
MSC:
| 13C10 | Projective and free modules and ideals in commutative rings |
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