【内容简介】
This book is mainly designed for the graduate students who axe in-terested in the theory of BCK and BCI-algebras. .
BCI-algebras axe a wider class than BCK-algebras, introduced by Kiyoshi Iseki in 1966. BCI-algebras as a class of logical algebras axe the algebraic formulations of the set difference together with its pro-perties in set theory and the implicational functor in logical systems.They are: closely related to partially ordered commutative monoids as well 'as various logical algebras. Their names axe originated from the combinators B, C, K and I in combinatory logic. The early re-search work was mainly carried out among the Japanese mathemati-cians Kiyoshi Iseki and Shotaxo Tanaka, etc. who did a great deal of foundation work. Since late 1970s, their work has been paid much attention. In particular, the participation in the research of Polish mathematicians Tadeusz Traczyk amd Andrzej Wrofiski as well as Australian mathematician William H. Cornish, etc. is making this branch of algebra develop rapidly. Many interesting and important results are discovered continuously. Now, the theory of BCI-algebras has been widely spread. ...
【目录】
     Chapter 0 Introduction
      0.1 Mappings Abelian Groups Binary Relations
      0.2 Lattices Boolean Algebras
      Chapter 1 General Theroy
      1.1 Definition and Elementary Properties
      1.2 BCK-Algebras
      1.3 p-Semisimple Algebras
      1.4 Ideals
      1.5 Congruences and Quotient Algebras
      1.6 BCI-Homomorphisms
      1.7 Direct Sums and Direct Products
      Chapter 2 Commutative BCK-Algebras
      2.1 Definition and Elementary Properties
      2.2 Commutative BCK-Lattices
      2.3 Structures of Certain Commutative BCK-Algebras
      2.4 Generalized Commutative BCK-Algebras
      2.5 Commutative Ideals
      2.6 Quasi-Commutative BCI-Algebras
      Chapter 3 Positive Implicativecand Implicative BCK-Algebras
      3.1 Positive Implicative BCK-Algebras
      3.2 Implicative BCK-Algbras
      3.3 Positive Implicativecand Implicative BCI-Algeberas
      3.4 Positive Implicative Ideals
      3.5 Implicative Ideals
      Chapter 4 BCI-Algebrascwith Condition(S)
      4.1 Definitioncand Elementary Properties
      4.2 Commutative BCK-Algebrascwith Condition(S)
      4.3 Positive Implicative BCK-Algebrascwith Condition(S)
      4.4 Implicative BCK-Algebrascwith Condition(S)
      4.5 Commutative Residual Pomonoids
      Chapter 5 Normal BCI-Algebras
      5.1 Simple BCI-Algebras
      5.2 Semisimple BCI-Algebras
      5.3 J-Semisimple BCI-Algebras
      5.4 Normal BCI-Algebras
      5.5 Normal Idealscin BCK-Algebras
      Chapter 6 Radicalscand Ideals
      6.1 Radicals
      6.2 p-Semisimple Ideals
      6.3 Associativecand Quasi-Associative Ideals
      6.4 Irreducible Ideals
      Appendix A
      Appendix B
      Bibliography
      Index...