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Abelian group in a topos of sheaves: torsion and essential extensions

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  • Kiran R. Bhutani

Abstract

We investigate the properties of torsion groups and their essential extensions in the category AbShL of Abellan groups in a topos of sheaves on a locale. We show that every torsion group is a direct sum of its p-primary components and for a torsion group A, the group [A,B] is reduced for any B ε AbShL.. We give an example to show that in AbShL the torsion subgroup of an injective group need not be injective. Further we prove that if the locale is Boolean or finite then essential extensions of torsion groups are torsion. Finally we show that for a first countable hausdorff space X essential extensions of torsion groups in AbSh0(X) are torsion iff X is discrete.

Suggested Citation

  • Kiran R. Bhutani, 1989. "Abelian group in a topos of sheaves: torsion and essential extensions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:272468
    DOI: 10.1155/S0161171289000128
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