Finitary and Artinian-Finitary Groups over the Integers ℤ
In a series of papers, we have considered finitary (that is, Noetherian-finitary) and Artinian-finitary groups of automorphisms of arbitrary modules over arbitrary rings. The structural conclusions for these two classes of groups are really very similar, especially over commutative rings. The questi...
Збережено в:
| Дата: | 2002 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2002
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/164055 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Finitary and Artinian-Finitary Groups over the Integers ℤ / B.A.F. Wehrfritz // Український математичний журнал. — 2002. — Т. 54, № 6. — С. 753–763. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | In a series of papers, we have considered finitary (that is, Noetherian-finitary) and Artinian-finitary groups of automorphisms of arbitrary modules over arbitrary rings. The structural conclusions for these two classes of groups are really very similar, especially over commutative rings. The question arises of the extent to which each class is a subclass of the other.
Here we resolve this question by concentrating just on the ground ring of the integers ℤ. We show that even over ℤ neither of these two classes of groups is contained in the other. On the other hand, we show how each group in either class can be built out of groups in the other class. This latter fact helps to explain the structural similarity of the groups in the two classes. |
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