| BCH-代数的首行商代数和不变子代数 |
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| 引用本文： | 李金龙.BCH-代数的首行商代数和不变子代数[J].安徽大学学报(自然科学版),2017,41(1). |
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| 作者姓名： | 李金龙 |
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| 作者单位： | 陕西理工大学 数学与计算机科学学院,陕西 汉中,723000 |
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| 基金项目： | 陕西省教育厅专项科学研究计划基金资助项目 |
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| 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*yx*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.
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| 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 |
First line quotient algebras and invaiant subalgebras of BCH-algebras |
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| LI Jinlong.First line quotient algebras and invaiant subalgebras of BCH-algebras[J].Journal of Anhui University(Natural Sciences),2017,41(1). |
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| Authors: | LI Jinlong |
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| Abstract: | A very convenient methed seeking the quotient algebra of a BCH-algebra was given in this paper,that 0*x=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. |
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| Keywords: | BCH-algebra generalized associative BCI-algebra first line quotient algebra invariant subalgebra distributive lattice |
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