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Cotorsion Theories and Colocalization

  • R. J. McMaster (a1)

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Let R be an associative ring with unit element. Mod-R and R-Mod will denote the categories of unitary right and left R-modules, respectively, and all modules are assumed to be in Mod-R unless otherwise specified. For all M, N ϵ Mod-R, HomR(M, N) will usually be abbreviated as [M, N]. For the definitions of basic terms, and an exposition on torsion theories in Mod-R, the reader is referred to Lambek [6]. Jans [5] has called a class of modules which is closed under submodules, direct products, homomorphic images, group extensions, and isomorphic images a TTF (torsion-torsionfree) class.

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References

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1. Azumaya, G., Some properties of TTF-classes, Proc. Conf. on Orders, Group Rings, and Related Topics, Lecture Notes in Math. 353 (Springer-Verlag, Berlin, 1973).
2. Chase, S. U., Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457473.
3. Courter, R. C., The maximal co-rational extension by a module, Can. J. Math. 18 (1966), 953962.
4. Gabriel, P., Des categories abeliennes, Bull. Soc. Math. France 90 (1962), 323448.
5. Jans, J. P., Some aspects of torsion, Pacific J. Math. 15 (1965), 12491259.
6. Lambek, J., Torsion theories, additive semantics, and rings of quotients, Lecture Notes in Math. 177 (Springer-Verlag, Berlin, 1971).
7. Lambek, J., Bicommutators of nice infectives, J. Algebra 21 (1972), 6073.
8. Lambek, J., Localization and completion, J. Pure Appl. Algebra 2 (1972), 343370.
9. Lambek, J. and Rattray, B., Localization at infectives in complete categories, Proc. Amer. Math. Soc. 41 (1973), 19.
10. Miller, R. W., TTF classes and quasi-generators, Pacific J. Math. 51 (1974), 499507.
11. Rutter, E. A. Jr., Torsion theories over semi-perfect rings, Proc. Amer. Math. Soc. 34 (1972), 389395.
12. Sandomierski, F. L., Modules over the endomorphism ring of a finitely generated projective module, Proc. Amer. Math. Soc. 31 (1972), 2731.
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Cotorsion Theories and Colocalization

  • R. J. McMaster (a1)

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