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Homology and Ringoids. III

  • P. J. Hilton and W. Ledermann

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The ringoids discussed in the preceding paper of this series(3) are characterized by two axioms which permit the operations of an exact category to be carried out within the structure of the ringoid. These operations do not in general include the formation of direct sums or products, for which new axioms are required. For a finite number of constituents these axioms are equivalent to the corresponding axiom in Buchsbaum's paper(1).

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References

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(1)Buchsbaum, D. A.Exact categories and duality. Trans. Amer. Math. Soc. 80 (1955), 1.
(2)Grothendieck, A.Sur quelques points d'algèbre homologique. Tohoku Math. J. 9 (1957), 119.
(3)Hilton, P. J. and Ledermann, W.Homology and ringoids. II. Proc. Camb. Phil. Soc. 55 (1959), 149.
(4)Kan, D. M.Adjoint functors. Trans. Amer. Math. Soc. 87 (1958), 294.

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