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- W2103239511 abstract "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)." @default.
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- W2103239511 date "1974-01-01" @default.
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- W2103239511 title "Codivisible and Projective Covers" @default.
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- W2103239511 doi "https://doi.org/10.1080/00927877408548607" @default.
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