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Injective and flat covers, envelopes and resolvents. (English) Zbl 0464.16019


MSC:

16D80 Other classes of modules and ideals in associative algebras
16D40 Free, projective, and flat modules and ideals in associative algebras
16Exx Homological methods in associative algebras
16D50 Injective modules, self-injective associative rings
16P40 Noetherian rings and modules (associative rings and algebras)
13H05 Regular local rings
18B30 Categories of topological spaces and continuous mappings (MSC2010)
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References:

[1] Bass, H., Finitistic dimension and a homological generalization of semiprimary rings, Trans. Amer. Math. Soc., 95, 466-488 (1960) · Zbl 0094.02201
[2] Bass, H., On the ubiquity of Gorenstein rings, Math. Z., 82, 8-28 (1963) · Zbl 0112.26604
[3] Enochs, E., Torsion free covering modules, Proc. Amer. Math. Soc., 14, 884-889 (1963) · Zbl 0116.26003
[4] P. Gabriel,Objects injectifs dans les Catégories abéliennes, Sém. Dubreil, 1958/59. · Zbl 0214.03301
[5] Northcott, D. G., Injective envelopes and inverse polynomials, J. London Math. Soc., 68, 290-296 (1974) · Zbl 0284.13012
[6] Oberst, U.; Röhrl, H., Flat and coherent functors, J. Algebra, 14, 91-105 (1970) · Zbl 0186.03003
[7] Switzer, R., Algebraic Topology—Homotopy and Homology (1975), Berlin, Heidelberg, New York: Springer-Verlag, Berlin, Heidelberg, New York · Zbl 0305.55001
[8] Teply, M., Torsion-free covers II, Israel J. Math., 23, 132-135 (1976) · Zbl 0321.16014
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