| FI代数同构于一族全序FI代数的直积的子代数的条件 |
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| 引用本文： | 刘练珍,李开泰.FI代数同构于一族全序FI代数的直积的子代数的条件[J].纯粹数学与应用数学,2004,20(1):63-67. |
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| 作者姓名： | 刘练珍 李开泰 |
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| 作者单位： | 西安交通大学理学院,西安,710049 |
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| 摘 要： | 解决了王国俊教授提出的关于FI代数的嵌入问题,并进一步研究了FI代数与一族全序FI代数的直积的子代数同构的条件.主要结果是:交换FI代数可同构嵌入一族全序交换FI代数的直积;分配FI代数可同构嵌入一族全序分配FI代数的直积.
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| 关 键 词： | FI代数 正则FI代数 交换FI代数 分配FI代数 直积 滤子 |
| 文章编号： | 1008-5513(2004)01-0063-05 |
| 修稿时间： | 2003年3月3日 |
The conditions of FI algebra to be a subalgebra of direct product of a system of linearly ordered FI algebras |
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| LIU Lian-zhen,LI Kai-tai.The conditions of FI algebra to be a subalgebra of direct product of a system of linearly ordered FI algebras[J].Pure and Applied Mathematics,2004,20(1):63-67. |
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| Authors: | LIU Lian-zhen LI Kai-tai |
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| Abstract: | We solve the problem proposed by Wang; moreover, the conditions of FI algebra to be a subalgebra of direct product of a system of linearly ordered FI algebras are investigated. The main results are: Each Commutative FI algebra can be embedded into direct product of a system of linearly ordered Commutative FI algebras; each Distributive FI algebra can be embedded into direct product of a system of linearly ordered Distributive FI algebras. |
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| Keywords: | FI algebra Regular FI algebra Commutative FI algebra Distributive FI algebra Direct product Filter |
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