COMPOSITION-DIAMOND LEMMA FORA-DIFFERENTIAL ASSOCIATIVE ALGEBRAS WITHMULTIPLE OPERATORS

JIANJUN QIU; YUQUN CHEN

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COMPOSITION-DIAMOND LEMMA FORA-DIFFERENTIAL ASSOCIATIVE ALGEBRAS WITHMULTIPLE OPERATORS

机译：具有多个算子的组合钻石微分微分联想代数

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In this paper, we establish the Composition-Diamond lemma for A-differential associativealgebras over a field K with multiple operators. As applications, we obtain Crobner-Shirshov bases of free A-differential Rota-Baxter algebras. In particular, linear basesof free λ-differential Rota-Baxter algebras are obtained and consequently, the free A-differential Rota-Baxter algebras are constructed by words.

机译：在本文中，我们建立了具有多个算子的场K上的A-微分关联代数的Composition-Diamond引理。作为应用，我们获得了免费的A微分Rota-Baxter代数的Crobner-Shirshov基。尤其是，获得了自由λ微分Rota-Baxter代数的线性底，因此，用单词构造了自由A微分Rota-Baxter代数。

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《Journal of algebra and its applications》 |2010年第2期|共17页
作者
JIANJUN QIU; YUQUN CHEN;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
A-differential Rota-Baxter algebra; A-differential associative algebra withmultiple operators; Grobner-Shirshov basis;

机译：A-微分Rota-Baxter代数;具有多个算子的A-微分联想代数;Grobner-Shirshov基;

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专利

1. COMPOSITION-DIAMOND LEMMA FORA-DIFFERENTIAL ASSOCIATIVE ALGEBRAS WITHMULTIPLE OPERATORS [J] . JIANJUN QIU, YUQUN CHEN Journal of algebra and its applications . 2010,第2期

机译：具有多个算子的组合钻石微分微分联想代数
2. Composition-Diamond Lemma for associative conformal algebras [J] . Bokut LA., Fong Y., Ke WF. Journal of Algebra . 2004,第2期

机译：组成-保形代数的钻石引理
3. Composition-Diamond lemma for tensor product of free algebras [J] . Bokut LA, Chen YQ, Chen YS Journal of Algebra . 2010,第9期

机译：自由代数张量积的成分-钻石引理
4. On Rota's Problem for Linear Operators in Associative Algebras [C] . Li Guo, William Y. Sit, Ronghua Zhang Proceedings of the 36th international symposium on symbolic and algebraic computation. . 2011

机译：关联代数中线性算子的Rota问题
5. THE ALGEBRA OF POLYNOMIAL FUNCTIONS ON A NON-ASSOCIATIVE ALGEBRA. [D] . FINSTON, DAVID ROBERT. 1983

机译：非缔合代数上的多项式函数的代数。
6. Rota–Baxter operators and post-Lie algebra structures on semisimple Lie algebras [O] . Dietrich Burde, Vsevolod Gubarev -1

机译：半简单李代数上的Rota–Baxter算子和后李代数结构
7. Composition-Diamond lemma for λ-differential associative algebras with multiple operators [O] . Jianjun Qiu, Yuqun Chen 2009

机译：具有多个算子的λ-微分联想代数的组合 - 金刚石引理

COMPOSITION-DIAMOND LEMMA FORA-DIFFERENTIAL ASSOCIATIVE ALGEBRAS WITHMULTIPLE OPERATORS

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