期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1989
卷号：12
DOI：10.1155/S0161171289000128
出版社：Hindawi Publishing Corporation
摘要：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 Bε
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.
