BCH-代数的首行商代数和不变子代数  

First line quotient algebras and invaiant subalgebras of BCH-algebras

作　　者：李金龙[1] 

机构地区：[1]陕西理工大学数学与计算机科学学院,陕西汉中723000

出　　处：《安徽大学学报（自然科学版）》2017年第1期47-52,共6页Journal of Anhui University(Natural Science Edition)

基　　金：陕西省教育厅专项科学研究计划基金资助项目(16JK1165)

摘　　要：给出一种求BCH-代数商代数的十分方便的方法,证明了0*x=0*yx*y∈B(X),并给出一个BCH-代数成为广义结合BCI-代数的两个条件.在BCH-代数中提出不变子代数的概念,证明了一个BCH-代数的两个不变子代数的交和并仍然是一个不变子代数,〈Q(X),∪,∩〉是一个分配格,其中Q(X)是一个BCH-代数中所有不变子代数做成的集合.A very convenient methed seeking the quotient algebra of a BCH-algebra was given in this paper, that 0 ＊ z=0 ＊ y if and only if x ＊ y∈B（X） was proved in a BCH-algebra （X; ＊ ,0）, two conditions that a BCH-algebra turned into a generalized associative BCI-algebra were given. The notion of invariant subalgebra was raised in the BCH-algebra, it was proved that the intersection and union of two invariant subalgebras in a BCH-algebra was an invariant subalgebra, and （Q（X）, ∪,∩） was a distributive lattice, where Q（X） was a set of all invariant subalgebras in a BCH-algebra.

关 键 词：BCH-代数 广义结合BCI-代数 首行商代数 不变子代数 分配格 

分 类 号：O152[理学—数学]