BCI-代数链复形的同调代数

本文在BCI-代数的正规链复形和链映射概念的基础上,引入了BCI-代数的同调代数的概念,得到了一些结果,尤其得到了BCI-同调代数的同构不变性。本文还给出了一类正规链复形—结合BCI-代数链复形。本文的一些结果可应用于对合群、Boole代数、幂集代数(运算是对称差)这三类代数,分别得到相应的同调代数的一些结果。

THE HOMOLOGICAL ALGEBRAS OF CHAIN COMPLEXES OF BCI-ALGEBRAS

In this paper the author has done some basic discussion for BCI-algebras with the method of homological algebras. On the basis of the concepts on the normal chain complexes and the chain mappings of BCI-algebras the author further introduced the concept of homological algebras of BCI-algebras. In the paper the author has done some discussion for the properties of BCI-homological algebras, and has got some results, especially isomorphic invariance of BCI-homological algebras. In the paper the au- thor has shown that there are normal chain complexes. Except trivial chain complexes, he also has given out a class of normal chain complexes--associative BCI-algebraic chain complexes.