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On products of modules in a topos

  • Javad Tavakoli (a1)

Abstract

In an elementary topos if R is a ring and X is a decidable object then there exists a canonical homomorphism from the coproduct of an X-family of R-modules to the product of the same family. In this paper it is shown that this homomorphisms is a monomorphism.

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Copyright

References

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[1]Harting, R., ‘Internal coproduct of Abelian groups in an elementary topos,’ Comm. in Alg. 10 (11), 11731237 (1982).
[2]Johnstone, P., Topos theory (L. M. S. Mathematical Monographs No. 10, Academic Press, 1977).
[3]Paré, R. and Schumacher, D., ‘Abstract families and the adjoint functor theorems’ (Indexed Categories and their Application, Springer Lecture Notes in Math. 661 (1978)), 1–125.
[4]Tavakoli, J., Vector spaces in topoi, Ph.D., thesis, Daihousie University, Canada (1980).
[5]Tavakoli, J., ‘Elements of free modules in topoi’, Comm. in Alg. 10(2) 171201 (1982).
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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