FI代数同构于一族全序FI代数的直积的子代数的条件  

The conditions of FI algebra to be a subalgebra of direct product of a system of linearly ordered FI algebras

作　　者：刘练珍[1] 李开泰[1] 

机构地区：[1]西安交通大学理学院,西安710049

出　　处：《纯粹数学与应用数学》2004年第1期63-67,共5页Pure and Applied Mathematics

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.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.

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 

分 类 号：O159[理学—数学]