| BCI-algebras which were raised in 1966 by K.Iseki, Japanese mathematician, are a wider class than BCK-algebras. With the development of nearly twenty years, BCI-algebras theory have became an important branch of general algebra. The hyperstruc-true theory was introduced in 1934 by F.Marty , several authors worked on it such that many branches of hyperstructrue theory appeared, such as hypergroup , hyperring , hyperBCK-algebras, hyperlatticet and so on. Hyperstructrues have many applications to several sectors of both pure and applied sciences. X.L.Xin firstly introduced the concept of hyper BCI-algebras in 2006, and investigated some related properties. It deversed us much research on hyper BCI-algebras.In this paper, some characteristics of hyper BCI-algebras and hyper~*BCI-algebras were investigated, the following several aspects are mainly discussed.In the chapter 2nd, we investigated operations of four kinds of hyperBCI-ideals, and discussed the relations between hyper BCI-algebras and properties of the homo-morphic preimage (image) of all kinds of hyper BCI-ideals.In the chapter 3rd, quotient hyper-algebras of hyper~*BCI-algebras were mainly investigated, the concept of hyperBCI-algebras was revised, and the concept of hyper*BCI-algebras was introduced. Furthermore, the concepts of left or right extension of hyper~*BCI-algebras were introduced, to build coset of hyper~*BCI-algebras, positive definite transposition hyper~*BCI-algebras and equivalent modulo N were also introduced, quotient hyper-algebras of hyper~*BCI-algebras were studied.In the chapter 4th, Given applications of quotient hyper-algebras of hyper*BCI-algebras, the three isomorphism theorems and some other properties of its are ob tained. |
