Abelian group in a topos of sheaves: torsion and essential extensions
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 AbSh...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000128 |
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| _version_ | 1832547986318557184 |
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| author | Kiran R. Bhutani |
| author_facet | Kiran R. Bhutani |
| author_sort | Kiran R. Bhutani |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-562310bb5ea846af83074227395be380 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-562310bb5ea846af83074227395be3802025-02-03T06:42:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-01121899810.1155/S0161171289000128Abelian group in a topos of sheaves: torsion and essential extensionsKiran R. Bhutani0Department of Mathematics, The Catholic University of America, Washington, D.C. 20064, USAWe 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.http://dx.doi.org/10.1155/S0161171289000128 |
| spellingShingle | Kiran R. Bhutani Abelian group in a topos of sheaves: torsion and essential extensions International Journal of Mathematics and Mathematical Sciences |
| title | Abelian group in a topos of sheaves: torsion and essential extensions |
| title_full | Abelian group in a topos of sheaves: torsion and essential extensions |
| title_fullStr | Abelian group in a topos of sheaves: torsion and essential extensions |
| title_full_unstemmed | Abelian group in a topos of sheaves: torsion and essential extensions |
| title_short | Abelian group in a topos of sheaves: torsion and essential extensions |
| title_sort | abelian group in a topos of sheaves torsion and essential extensions |
| url | http://dx.doi.org/10.1155/S0161171289000128 |
| work_keys_str_mv | AT kiranrbhutani abeliangroupinatoposofsheavestorsionandessentialextensions |