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BCI-algebra. (Chinese) Zbl 0675.06013

Xi’an (China): Shannxi Scientific and Technical Publishing House. 492 p. (1987).
In 1966, Y. Imai and K. Iséki introduced BCK-algebras and BCI-algebras. Now, in Japan, Poland, USA, Czechoslovakia, Australia, Libia, Sudan, Sri Lanka, India, Pakistan and China, many mathematicians study these kinds of algebras and have obtained results.
This book is the first book on BCI-algebras. It consists of 8 chapters. In the first chapter, the author introduces some preparatory material, in the second chapter BCK-algebras are introduced, and in the third chapter the author considers some concepts and properties of BCI-algebras. In the fourth chapter, the following topics are treated: quasi-commutative BCI- algebras, the variety of BCI-algebras, BCI-algebras with the condition (S), and radical properties of BCI-algebras. In the fifth chapter, the important topic of associative BCI-algebras is considered and, moreover, generalized associative BCI-algebras, and BCI-algebras with the discrete sub-algebra property. In the sixth chapter the author introduces BCK- and BCI-topological algebras. The seventh chapter treats BCH-algebras, which were introduced by the author in 1981. In the eighth chapter the author deals with his views on the further development of BCK-, BCI-, and BCH- algebras.
Reviewer: Hu Qingping

MSC:

06F99 Ordered structures
06-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures
08A99 Algebraic structures
08C99 Other classes of algebras
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