泛代数上的Groebner-Shirshov基理论

基金项目:

国家自然科学基金;教育部博士点基金;俄罗斯科学基金

详细信息

Gr\"{o}bner-Shirshov Bases for Universal Algebras

Funds:

;Doctoral Program of Higher Education of China;Russian Science Fund

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．
- Ω-代数
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.
- $\Omega$ -algebra

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