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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147858 |
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| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862648145120329728 |
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| author | Manea, A. Ştefan, D. |
| author_facet | Manea, A. Ştefan, D. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-01T14:19:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147858 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T14:19:49Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Manea, A. Ştefan, D. 2019-02-16T09:24:43Z 2019-02-16T09:24:43Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/147858 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. Both authors were financially supported by CNCS-UEFISCDI, project PCE PN-II-ID-PCE2011-3-0635. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Further Properties and Applications of Koszul Pairs Article published earlier |
| spellingShingle | Further Properties and Applications of Koszul Pairs Manea, A. Ştefan, D. |
| title | 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_short | Further Properties and Applications of Koszul Pairs |
| title_sort | further properties and applications of koszul pairs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147858 |
| work_keys_str_mv | AT maneaa furtherpropertiesandapplicationsofkoszulpairs AT stefand furtherpropertiesandapplicationsofkoszulpairs |