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| Titel: |
Codivisible and Projective Covers |
| Auteur: |
Teply, Mark L. |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 1 (1974) nr. 1 pagina's 23-38 |
| Jaar: |
1974 |
| Inhoud: |
This paper continues the study of codivisible modules, whose definition is a “dualization” of Lambek's concept [4] of a divisible module relative to a torsion theory. The main purpose of this work is to give a solution to the following problem posed by Bland [2]: “It would be interesting to know under what conditions the universal existence of codivisible covers implies that of projective covers.” The if-and-only-if nature of the solution, which is given in Theorems 2 and 4, shows that our sufficient conditions are “best possible” conditions. The method of the solution introduces the concept of a pseudo-hereditary torsion theory, which may be of interest in its own right; in particular, every hereditary torsion theory and every faithful torsion theory is pseudo-hereditary. The main results for a pseudo-hereditary torsion theory (T, F) relate the conditions, R/T(R) is semiperfect and R/T(R) is left perfect, to the existence of codivisible covers (see Theorems 1 and 3 and Corollaries 1 and 2). |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 2 van 5 gevonden artikelen
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