Steadiness of polynomial rings
A module M is said to be small if the functor Hom(M,−) commutes with direct sums and right steady rings are exactly those rings whose small modules are necessary finitely generated. We give several results on steadiness of polynomial rings, namely we prove that polynomials over a right perfect ring...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2010 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/154871 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Steadiness of polynomial rings / J. Zemlicka // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 107–117. — Бібліогр.: 13 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639452042559488 |
|---|---|
| author | Zemlicka, J. |
| author_facet | Zemlicka, J. |
| citation_txt | Steadiness of polynomial rings / J. Zemlicka // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 107–117. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A module M is said to be small if the functor Hom(M,−) commutes with direct sums and right steady rings are exactly those rings whose small modules are necessary finitely generated. We give several results on steadiness of polynomial rings, namely we prove that polynomials over a right perfect ring such that EndR(S) is finitely generated over its center for every simple module S form a right steady ring iff the set of variables is countable. Moreover, every polynomial ring in uncountably many variables is non-steady.
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| first_indexed | 2025-12-01T01:23:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154871 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| language | English |
| last_indexed | 2025-12-01T01:23:14Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Zemlicka, J. 2019-06-16T05:56:46Z 2019-06-16T05:56:46Z 2010 Steadiness of polynomial rings / J. Zemlicka // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 107–117. — Бібліогр.: 13 назв. — англ. 2000 Mathematics Subject Classification:16S36, 16D10. https://nasplib.isofts.kiev.ua/handle/123456789/154871 A module M is said to be small if the functor Hom(M,−) commutes with direct sums and right steady rings are exactly those rings whose small modules are necessary finitely generated. We give several results on steadiness of polynomial rings, namely we prove that polynomials over a right perfect ring such that EndR(S) is finitely generated over its center for every simple module S form a right steady ring iff the set of variables is countable. Moreover, every polynomial ring in uncountably many variables is non-steady. This work is part of the research project MSM 0021620839, financed by MŠMT. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Steadiness of polynomial rings Article published earlier |
| spellingShingle | Steadiness of polynomial rings Zemlicka, J. |
| title | Steadiness of polynomial rings |
| title_full | Steadiness of polynomial rings |
| title_fullStr | Steadiness of polynomial rings |
| title_full_unstemmed | Steadiness of polynomial rings |
| title_short | Steadiness of polynomial rings |
| title_sort | steadiness of polynomial rings |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154871 |
| work_keys_str_mv | AT zemlickaj steadinessofpolynomialrings |