Title :
Solution of Three Open Problems on Pseudo-Filters (Pseudo-Ideals) of Pseudo-BCK Algebras
Author :
Zhang, Xiaohong ; Jun, Young Bae
Author_Institution :
Dept. of Math., Shanghai Maritime Univ., Shanghai, China
Abstract :
Three open problems on pseudo-filters (ideals) of pseudo-BCK algebras, posed by Y.B. Jun, M. Kondo and K.H. Kim [Pseudo-ideals of pseudo-BCK algebras, Scientiae Mathematicae Japonicae, 2003, 1: 93-97], are solved. Moreover, some properties of pseudo-BCK algebras and some examples are presented, and the following important result is proved: a pseudo-BCK algebra becomes a positive implicative BCK-algebra if and only if its every pseudo-filter (ideals) is a normal positive implicative pseudo-filter (ideal).
Keywords :
algebra; formal logic; positive implicative pseudofilter; pseudo BCK algebra; pseudoideals; three open problem; Algebra; Calculus; Electronic mail; Fuzzy logic; Noise measurement; Quantum computing; normal pseudo-filter; positive implicative BCK-algebra; pseudo-BCK algebra; pseudo-filter (ideal);
Conference_Titel :
Artificial Intelligence and Computational Intelligence (AICI), 2010 International Conference on
Conference_Location :
Sanya
Print_ISBN :
978-1-4244-8432-4
DOI :
10.1109/AICI.2010.231
