Abstract
A ring R is regular [completely reducible] if and only if the character module of every left A-module is quasiinjective [quasiprojective]. Submodules of quasiprojective left if-modules over a left perfect ring R are quasiprojective if and only if singular left 7?-modules are injective. A splitting theorem for right perfect rings over which submodules of quasiprojective left i?-modules are quasiprojective is also proven. These results continue the author's previous work ([5] and [6]).
| Original language | English |
|---|---|
| Pages (from-to) | 401-408 |
| Number of pages | 8 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 31 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1972 |
| Externally published | Yes |
Keywords
- Character module
- Completely reducible ring
- Hereditary ring
- Perfect ring
- Quasiprojective module
- Regular ring
- Semihereditary ring
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics