BCI-代數(shù)

內(nèi)容概要

This book is mainly designed for the graduate students who are in-terested in the theory of BCK and BCI-algebras.　　BCI-algebras are a wider class than BCK-algebras, introduced by　Kiyoshi Iseki in 1966. BCI-algebras as a class of logical algebras are　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 are 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 Is~ki and Shotaro　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 and Andrzej Wronski 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.

書籍目錄

Chapter 0  Introduction　0.1  Mappings Abelian Groups Binary Relations　0.2  Lattices Boolean AlgebrasChapter 1  General Theory　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 ProductsChapter 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-AlgebrasChapter 3  Positive Implicative and Implicative　BCK-Algebras　3.1  Positive Implicative BCK-Algebras　3.2  Implicative BCK-Algebras　3.3  Positive Implicative and Implicative BCI-Algebras　3.4  Positive Implicative Ideals　3.5  Implicative IdealsChapter 4  BCI-Algebras with Condition (S)　4.1  Definition and Elementary Properties　4.2  Commutative BCK-Algebras with Condition (S)　4.3  Positive Implicative BCK-Algebras with Condition (S)　4.4  Implicative BCK-Algebras with Condition (S)　4.5  Commutative Residual PomonoidsChapter 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 Ideals in BCK-AlgebrasChapter 6  Radicals and Ideals　6.1  Radicals　6.2  p-Semisimple Ideals　6.3  Associative and Quasi-Associative Ideals　6.4  Irreducible IdealsAppendix AAppendix BBibliographyIndex

編輯推薦

　　《BCI-代數(shù)》系統(tǒng)地介紹了BCI－代數(shù)的基礎(chǔ)理論，闡述了自BCI－代數(shù)問世以來國內(nèi)外尤其是國內(nèi)學(xué)者的主要研究成果。

圖書封面

評論、評分、閱讀與下載

---

    BCI-代數(shù) PDF格式下載

---