Distributed by Elsevier Science on behalf of Science Press.
This book is mainly designed for graduate students who are interested in the theory of BCK and BCI-algebras. It introduces the general theoretical basis of BCI-algebras, omitting difficult proofs and abstract topics which are less necessary for beginners to learn. With abundant examples and exercises arranged after each section, it provides readers with easy-to-follow steps into this field.
* Specially designed for graduate students with emphasis on elementary knowledge in this field
* Organizes knowledge points systematically and highlights various arguments on vital topics to make them easy to be understand
* Gives many examples to clarify important notations and terminologies and abundant of classified exercises after each chapter for revision purposes
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abelian group Assume BCI-homomorphism BCI-ordering BCK-algebra of order BCK-algebra with condition BCK-part binary operation Boolean algebra called commutative BCK-algebra commutative BCK-chain commutative BCK-lattice commutative ideal commutative law congruence Corollary Define a binary Definition Denote distributive lattice epimorphic Example Exercise exists finite order following are equivalent following holds greatest element Hasse diagram Hence I-congruence ideal of X irreducible ideals isomorphic Lemma lower BCK-semilattice lower semilattice mapping maximal ideal minimal element multiply commutative multiply implicative multiply positive implicative n-fold commutative n-fold implicative n-fold positive implicative natural number nonempty subset nonzero element obtain Obviously p-semisimple algebra partially ordered set pomonoid positive implicative BCK-algebra positive implicative ideal proper BCI-algebra proper ideal Proposition quasi-associative quotient algebra X/A r-ideal satisfies the following semilattice Show subalgebra subdirect product subdirect sum submonoid Suppose Theorem upper semilattice Verify x o y Yliei zero ideal