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...
Збережено в:
| Дата: | 2010 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
|
| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154871 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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| id |
irk-123456789-154871 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1548712019-06-17T01:31:16Z Steadiness of polynomial rings Zemlicka, J. 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. 2010 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/154871 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Zemlicka, J. |
| spellingShingle |
Zemlicka, J. Steadiness of polynomial rings Algebra and Discrete Mathematics |
| author_facet |
Zemlicka, J. |
| author_sort |
Zemlicka, J. |
| title |
Steadiness of polynomial rings |
| title_short |
Steadiness of polynomial rings |
| title_full |
Steadiness of polynomial rings |
| title_fullStr |
Steadiness of polynomial rings |
| title_full_unstemmed |
Steadiness of polynomial rings |
| title_sort |
steadiness of polynomial rings |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154871 |
| citation_txt |
Steadiness of polynomial rings / J. Zemlicka // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 2. — С. 107–117. — Бібліогр.: 13 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT zemlickaj steadinessofpolynomialrings |
| first_indexed |
2023-05-20T17:45:26Z |
| last_indexed |
2023-05-20T17:45:26Z |
| _version_ |
1796154014058938368 |