A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings
Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable polynomial algebras and (skew) PBW extensions....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2015-05-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2015-0028 |
| _version_ | 1818358412415598592 |
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| author | Zhao Xiangui Zhang Yang |
| author_facet | Zhao Xiangui Zhang Yang |
| author_sort | Zhao Xiangui |
| collection | DOAJ |
| description | Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative
polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial
rings, which are generalizations of solvable polynomial algebras and (skew) PBW extensions. Then we present a
signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings over fields. |
| first_indexed | 2024-12-13T20:28:35Z |
| format | Article |
| id | doaj.art-71e19eb807f149e6bfffb16f77e57713 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-13T20:28:35Z |
| publishDate | 2015-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-71e19eb807f149e6bfffb16f77e577132022-12-21T23:32:29ZengDe GruyterOpen Mathematics2391-54552015-05-0113110.1515/math-2015-0028math-2015-0028A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial ringsZhao Xiangui0Zhang Yang1Department of Mathematics, Huizhou University, Huizhou, Guangdong, 516007, China, E-mail: xiangui.zhao@foxmail.comDepartment of Mathematics, University of Manitoba, Winnipeg, R3T 2N2, Canada, E-mail: yang.zhang@umanitoba.caSignature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable polynomial algebras and (skew) PBW extensions. Then we present a signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings over fields.https://doi.org/10.1515/math-2015-0028gröbner-shirshov basis skew solvable polynomial ring signature-based algorithm |
| spellingShingle | Zhao Xiangui Zhang Yang A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings Open Mathematics gröbner-shirshov basis skew solvable polynomial ring signature-based algorithm |
| title | A signature-based algorithm for computing
Gröbner-Shirshov bases in skew solvable
polynomial rings |
| title_full | A signature-based algorithm for computing
Gröbner-Shirshov bases in skew solvable
polynomial rings |
| title_fullStr | A signature-based algorithm for computing
Gröbner-Shirshov bases in skew solvable
polynomial rings |
| title_full_unstemmed | A signature-based algorithm for computing
Gröbner-Shirshov bases in skew solvable
polynomial rings |
| title_short | A signature-based algorithm for computing
Gröbner-Shirshov bases in skew solvable
polynomial rings |
| title_sort | signature based algorithm for computing grobner shirshov bases in skew solvable polynomial rings |
| topic | gröbner-shirshov basis skew solvable polynomial ring signature-based algorithm |
| url | https://doi.org/10.1515/math-2015-0028 |
| work_keys_str_mv | AT zhaoxiangui asignaturebasedalgorithmforcomputinggrobnershirshovbasesinskewsolvablepolynomialrings AT zhangyang asignaturebasedalgorithmforcomputinggrobnershirshovbasesinskewsolvablepolynomialrings AT zhaoxiangui signaturebasedalgorithmforcomputinggrobnershirshovbasesinskewsolvablepolynomialrings AT zhangyang signaturebasedalgorithmforcomputinggrobnershirshovbasesinskewsolvablepolynomialrings |