On derivations of quantales
A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-01-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2016-0030 |
| _version_ | 1818716519919517696 |
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| author | Xiao Qimei Liu Wenjun |
| author_facet | Xiao Qimei Liu Wenjun |
| author_sort | Xiao Qimei |
| collection | DOAJ |
| description | A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation. |
| first_indexed | 2024-12-17T19:20:33Z |
| format | Article |
| id | doaj.art-fac7824c433642a08d7f171fd9f80f4e |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T19:20:33Z |
| publishDate | 2016-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-fac7824c433642a08d7f171fd9f80f4e2022-12-21T21:35:35ZengDe GruyterOpen Mathematics2391-54552016-01-0114133834610.1515/math-2016-0030math-2016-0030On derivations of quantalesXiao Qimei0Liu Wenjun1School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410004, P.R. ChinaSchool of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410004, P.R. ChinaA quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation.https://doi.org/10.1515/math-2016-0030quantalederivationquantic nucleuspre-derivationquantic pre-nucleus06a0654a10 |
| spellingShingle | Xiao Qimei Liu Wenjun On derivations of quantales Open Mathematics quantale derivation quantic nucleus pre-derivation quantic pre-nucleus 06a06 54a10 |
| title | On derivations of quantales |
| title_full | On derivations of quantales |
| title_fullStr | On derivations of quantales |
| title_full_unstemmed | On derivations of quantales |
| title_short | On derivations of quantales |
| title_sort | on derivations of quantales |
| topic | quantale derivation quantic nucleus pre-derivation quantic pre-nucleus 06a06 54a10 |
| url | https://doi.org/10.1515/math-2016-0030 |
| work_keys_str_mv | AT xiaoqimei onderivationsofquantales AT liuwenjun onderivationsofquantales |