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...
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| Date: | 2002 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4113 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510245718065152 |
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| author | Wehrfritz, B. A. F. Веґрфріц, Б. А. Ф. |
| author_facet | Wehrfritz, B. A. F. Веґрфріц, Б. А. Ф. |
| author_sort | Wehrfritz, B. A. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:22:38Z |
| description | 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. |
| first_indexed | 2026-03-24T02:53:56Z |
| format | Article |
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| id | umjimathkievua-article-4113 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:53:56Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/19/f8a014e8b62a038a13bfb896bd5ef419.pdf |
| spelling | umjimathkievua-article-41132020-03-18T20:22:38Z Finitary and Artinian-Finitary Groups over the Integers $ℤ$ Фінітарні та артиново-фінітарні групи над цілими числами $ℤ$ Wehrfritz, B. A. F. Веґрфріц, Б. А. Ф. 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. У низці робіт автора розглядались фінітарні (іобто нетерово-фінітарні) і аргипово-фінітарні групи автоморфізмів довільних модулів над довільними кільцями. Структурні висновки для цих двох класів груп дуже подібні, особливо у випадку комутативних кілець. Виникає питання про те, в якій мірі один з цих класів к підкласом іншого. У даній роботі цс питання вирішується па прикладі кільця чисел $ℤ$. Показано, що навіть Institute of Mathematics, NAS of Ukraine 2002-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4113 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 6 (2002); 753-763 Український математичний журнал; Том 54 № 6 (2002); 753-763 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/4113/4935 https://umj.imath.kiev.ua/index.php/umj/article/view/4113/4936 Copyright (c) 2002 Wehrfritz B. A. F. |
| spellingShingle | Wehrfritz, B. A. F. Веґрфріц, Б. А. Ф. Finitary and Artinian-Finitary Groups over the Integers $ℤ$ |
| title | Finitary and Artinian-Finitary Groups over the Integers $ℤ$ |
| title_alt | Фінітарні та артиново-фінітарні групи над цілими числами $ℤ$ |
| title_full | Finitary and Artinian-Finitary Groups over the Integers $ℤ$ |
| title_fullStr | Finitary and Artinian-Finitary Groups over the Integers $ℤ$ |
| title_full_unstemmed | Finitary and Artinian-Finitary Groups over the Integers $ℤ$ |
| title_short | Finitary and Artinian-Finitary Groups over the Integers $ℤ$ |
| title_sort | finitary and artinian-finitary groups over the integers $ℤ$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4113 |
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