Abstract
IfR is a strongly hereditary relative homological algebra of Abelian groups which contains the torsion split sequences, then theR-injectives can be completely characterized. IfR is a relative homological algebra with enough projectives and enough injectives, which contains the torsiol split sequences, then equivalent conditions forR to be strongly hereditary are given.
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Literatur
BUCHSBAUM, D.: A note on homology in categories, Ann. of Math. 69, 66–74 (1958).
HARRISON, D. K.: Infinite Abelian groups and homological methods, Ann. of Math. 69, 336–391 (1959).
IRWIN, J. W. WALKER, C., and WALKER, E. A.: On pα-pure sequences of Abelian groups, Topics in Abelian Groups, ed. by J. M. Irwin and E. A. Walker, Scott Foresman and Co., Chicago, 69–119 1963.
MACLANE, S.: Homology, Springer-Verlag, Berlin 1963.
NUNKE, R. J.: Purity and subfunctors of the identity, Topics in Abelian Groups, ed. by J. M. Irwin and E. A. Walker, Scott Foresman and Co., Chicago 121–171 1963.
WALKER, C. P.: Relative homological algebra and Abelian groups, Ill. J. Math. 10, 186–209 (1966).
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Cook, D. Injectives of strongly hereditary relative homological algebras. Manuscripta Math 1, 377–383 (1969). https://doi.org/10.1007/BF01172143
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DOI: https://doi.org/10.1007/BF01172143