Further Properties and Applications of Koszul Pairs
Koszul pairs were introduced in [arXiv:1011.4243] as an instrument for the study of Koszul rings. In this paper, we continue the enquiry of such pairs, focusing on the description of the second component, as a follow-up of the study in [arXiv:1605.05458]. As such, we introduce Koszul corings and pro...
Збережено в:
| Дата: | 2016 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147858 |
| 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: | Further Properties and Applications of Koszul Pairs / A. Manea, D. Ştefan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147858 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1478582019-02-17T01:27:22Z Further Properties and Applications of Koszul Pairs Manea, A. Ştefan, D. Koszul pairs were introduced in [arXiv:1011.4243] as an instrument for the study of Koszul rings. In this paper, we continue the enquiry of such pairs, focusing on the description of the second component, as a follow-up of the study in [arXiv:1605.05458]. As such, we introduce Koszul corings and prove several equivalent characterizations for them. As applications, in the case of locally finite R-rings, we show that a graded R-ring is Koszul if and only if its left (or right) graded dual coring is Koszul. Finally, for finite graded posets, we obtain that the respective incidence ring is Koszul if and only if the incidence coring is so. 2016 Article Further Properties and Applications of Koszul Pairs / A. Manea, D. Ştefan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16E40; 16T10; 16T15 DOI:10.3842/SIGMA.2016.092 http://dspace.nbuv.gov.ua/handle/123456789/147858 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Koszul pairs were introduced in [arXiv:1011.4243] as an instrument for the study of Koszul rings. In this paper, we continue the enquiry of such pairs, focusing on the description of the second component, as a follow-up of the study in [arXiv:1605.05458]. As such, we introduce Koszul corings and prove several equivalent characterizations for them. As applications, in the case of locally finite R-rings, we show that a graded R-ring is Koszul if and only if its left (or right) graded dual coring is Koszul. Finally, for finite graded posets, we obtain that the respective incidence ring is Koszul if and only if the incidence coring is so. |
| format |
Article |
| author |
Manea, A. Ştefan, D. |
| spellingShingle |
Manea, A. Ştefan, D. Further Properties and Applications of Koszul Pairs Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Manea, A. Ştefan, D. |
| author_sort |
Manea, A. |
| title |
Further Properties and Applications of Koszul Pairs |
| title_short |
Further Properties and Applications of Koszul Pairs |
| title_full |
Further Properties and Applications of Koszul Pairs |
| title_fullStr |
Further Properties and Applications of Koszul Pairs |
| title_full_unstemmed |
Further Properties and Applications of Koszul Pairs |
| title_sort |
further properties and applications of koszul pairs |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147858 |
| citation_txt |
Further Properties and Applications of Koszul Pairs / A. Manea, D. Ştefan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 17 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT maneaa furtherpropertiesandapplicationsofkoszulpairs AT stefand furtherpropertiesandapplicationsofkoszulpairs |
| first_indexed |
2023-05-20T17:28:41Z |
| last_indexed |
2023-05-20T17:28:41Z |
| _version_ |
1796153391003467776 |