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Sous-groupes fonctoriels et rélativisations. (French) Zbl 0246.20048
MSC:
20K40 Homological and categorical methods for abelian groups
20J05 Homological methods in group theory
18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)
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References:
[1] BUCHSBAUM D. , A note on homology in categories , Ann. of Math. (2) vol. 69, ( 1959 ), p. 66-74. MR 25 #3974 | Zbl 0084.26801 · Zbl 0084.26801 · doi:10.2307/1970093
[2] BUTLER M.C.R. HORROCKS G. , Classes of extensions an resolutions . Philos. Trans. Roy. Soc. London, vol. 254, ( 1961 ), p. 155-222. MR 32 #5706 | Zbl 0099.25902 · Zbl 0099.25902 · doi:10.1098/rsta.1961.0014
[3] CHARLES B. , Sous-groupes fonctoriels et topologies , Etudes sur les groupes abéliens, p. 75-92, Dunod, Paris ( 1968 ). MR 39 #1547 | Zbl 0179.32701 · Zbl 0179.32701
[4] COOK D. , Relative homological algebra in the category of abelian groups , Thèse New-Mexico State University ( 1968 ).
[5] EILENBERG S. MOORE J.C. Foundations of relative homological algebra . Memoirs of the Amer. Math. Soc. n^\circ 55 ( 1965 ). MR 31 #2294 | Zbl 0129.01101 · Zbl 0129.01101
[6] FUCHS L. , Abelian groups , Publ. House of the Hungarian Academy of Sciences, Budapest ( 1958 ). MR 21 #5672 | Zbl 0091.02704 · Zbl 0091.02704
[7] FUCHS L. , Some generalizations of the exact sequences concerning Hom and Ext , Proc. of the Colloquium on Abelian groups Publ. House of the Hungarian Academy of Sciences, Budapest ( 1964 ). Zbl 0135.02204 · Zbl 0135.02204
[8] HARRISSON D.K. Infinite Abelian Groups and Homological Methods . Ann. of Math. vol. 69, p. 366-391, ( 1959 ). MR 21 #3481 | Zbl 0100.02901 · Zbl 0100.02901 · doi:10.2307/1970188
[9] HELLER A. Homological algebra in abelian categories . Ann. of Math. (2) vol. 68, p. 484-525 ( 1958 ). MR 20 #7051 | Zbl 0084.26704 · Zbl 0084.26704 · doi:10.2307/1970153
[10] HOCHSCHILD G. Relative homological algebra . Trans. Amer. Math. Soc., vol. 82, p. 246-269 ( 1956 ). MR 18,278a | Zbl 0070.26903 · Zbl 0070.26903 · doi:10.2307/1992988
[11] KAPLANSKY I. Infinite Abelian Groups , University of Michigan Press. Ann. Arbor ( 1954 ). MR 16,444g | Zbl 0057.01901 · Zbl 0057.01901
[12] MAC LANE S. Homology . Springer-Verlag Berlin ( 1963 ). MR 28 #122 | Zbl 0818.18001 · Zbl 0818.18001
[13] MARANDA J.M. Injective structures , Trans. Amer. Math. Soc. vol. 110 p. 98-135 ( 1964 ). MR 29 #1236 | Zbl 0121.26601 · Zbl 0121.26601 · doi:10.2307/1993639
[14] MARTY R. Radical , socle et relativisation, Etudes sur les groupes abéliens, p. 287-300 Dunod, Paris ( 1968 ). MR 39 #2840 | Zbl 0182.35701 · Zbl 0182.35701
[15] NUNKE R.J. Purity and subsfunctors of the identity . Topics in abelian groups. Scott Foresman Chicago p. 121-172 ( 1963 ). MR 30 #156
[16] STENSTROM BO. T. ”Pure submodules” Arkiv för Mat., 7, 159-171 ( 1967 ). MR 36 #6473 | Zbl 0153.34302 · Zbl 0153.34302 · doi:10.1007/BF02591032
[17] WALKER C.P. Relative homological algebra and abelian groups . Ill. Journal of Math. vol. 10 n^\circ 2, p. 186-209 ( 1966 ). MR 32 #7624 | Zbl 0136.25601 · Zbl 0136.25601
[18] WALKER C.P. , WALKER E.A. , IRWIN J.M. On palpha-pure sequences of abelian groups . Topics in abelian groups, Scott Foresman Chicago p. 69-119 ( 1963 ). MR 33 #7410
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