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Observations on the Künneth theorem

  • G. M. Kelly (a1)

Let A be a right Λ-complex and C be a left Λ-complex where Λ is a ring which is both left and right hereditary; a principal ideal domain is a special case of such a ring. This paper is concerned with the Künneth theorem expressing the homology H(A⊗C) of the product complex A⊗C (= A⊗ΛC) in terms of H(A) and H(C). Any notations we do not explain are those of (1).

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(1)Cartan, H. and Eilenberg, S., Homological algebra (Princeton, 1956).
(2)Eilenberg, S. and MacLane, S., On the groups H(π, n). II. Ann. of Math. 60 (1954), 49139.
(3)MacLane, S., Triple torsion products and multiple Künneth formulas. Math. Ann. 140 (1960), 5164.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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