| 自由Rota-Baxter代数的因子分解 |
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| 引用本文： | 张天杰,高兴,郭锂.自由Rota-Baxter代数的因子分解[J].数学学报,2017,60(5):789-798. |
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| 作者姓名： | 张天杰 高兴 郭锂 |
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| 作者单位： | 1. 宁夏大学数学统计学院 银川 750021;
2. 兰州大学数学与统计学院 兰州 730030;
3. 江西师范大学数学与信息学院 南昌 330022;
4. Rutgers大学数学与计算机科学系 纽瓦克 NJ 07102 |
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| 基金项目： | 国家自然科学基金（11371177，11371178）；山东省自然科学基金面上项目（ZR2016AM02）；兰州大学中央高校基本科研业务费专项资金助（lzujbky-2017-162） |
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| 摘 要： | 近年来,Rota-Baxter代数在数学和物理学中有着广泛的应用,受到越来越多的关注,自由Rota-Baxter代数分别用括号字,根树以及Motzkin路径得到了构造.因子分解在代数学中是一个很重要的问题.本文主要考虑用括号字构造的自由RotaBaxter代数,得到了自由Rota-Baxter代数中基元素的因子分解.
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| 关 键 词： | Rota-Baxter代数 不可约元素 因子分解 根树 |
Factorizations in Free Rota-Baxter Algebras |
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| Tian Jie ZHANG,Xing GAO,Li GUO.Factorizations in Free Rota-Baxter Algebras[J].Acta Mathematica Sinica,2017,60(5):789-798. |
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| Authors: | Tian Jie ZHANG Xing GAO Li GUO |
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| Institution: | 1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P. R. China;
2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730030, P. R. China;
3. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, P. R. China;
4. Department of Mathematics and Computer Science, Rutgers University, Newark NJ 07102, USA |
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| Abstract: | The study of Rota-Baxter algebras has attracted quite much attentions in recent years for their broad applications in mathematics and physics. Free Rota-Baxter algebras have been constructed by bracketed words, rooted trees and Motzkin paths.We focus on the construction by bracketed words for the convenience of computations. Factorization in algebra is an important problem. In this paper, we obtain a unique factorization of the basis elements in the free Rota-Baxter algebras of bracketed words. |
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| Keywords: | Rota-Baxter algebra indecomposable elements factorization rooted tree |
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