| 泛代数上的Groebner-Shirshov基理论 |
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| 引用本文： | L A Bokut,陈裕群. 泛代数上的Groebner-Shirshov基理论[J]. 华南师范大学学报(自然科学版), 2014, 46(6): 1-9 |
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| 作者姓名： | L A Bokut 陈裕群 |
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| 作者单位： | 1.华南师范大学数学科学学院 |
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| 基金项目： | 国家自然科学基金项目(11171118);教育部博士点基金项目(20114407110007);广东省高校国际科技合作创新平台(2012g jhz0007);俄罗斯科学基金项目(RSF,N 14-21-00065) |
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| 摘 要： | 综述了域上或交换代数上的线性（-）代数的相应的簇（范畴）的 Groebner-Shirshov 基理论的新成果,如:结合代数（包括群（半群）代数）,自由代数的张量积,李代数,Di-代数,pre-李代数,Rota-Baxter代数,metabelian李代数,L-代数,半环代数,范畴代数,等．以上结果包含了许多应用,尤其是给出了一些著名结论的新的证明．
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| 关 键 词： | Ω-代数 |
| 收稿时间： | 2014-09-16 |
Gr{o}bner-Shirshov Bases for Universal Algebras |
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| L A Bokut;Chen Yuqun. Gr{o}bner-Shirshov Bases for Universal Algebras[J]. Journal of South China Normal University(Natural Science Edition), 2014, 46(6): 1-9 |
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| Authors: | L A Bokut Chen Yuqun |
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| Affiliation: | L A Bokut;Chen Yuqun;School of Mathematical Sciences,South China Normal University;Sobolev Institute of Mathematics,Novosibirsk State University; |
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| Abstract: | Some results were reviewed in Gr{o}bner-Shirshov bases method for different varieties (categories) of linear ($Omega$-) algebras over a field $k$ or a commutative algebra $K$ over $k$: associative algebras (including group (semigroup) algebras), tensor product of free associative algebras, Lie algebras, dialgebras, pre-Lie (Vinberg right (left) symmetric) algebras, Rota-Baxter algebras, metabelian Lie algebras, $L$-algebras, semiring algebras, category algebras, etc. There are some applications particularly to new proofs of some known theorems. |
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