Title :
On the adjoint semigroup of a class of logical algebras
Author :
Minxia Luo ; Ni Sang
Author_Institution :
Sch. of Sci., China Jiliang Univ., Hangzhou, China
Abstract :
In this paper, a class of logical algebras were studied. Firstly, the characterization of a general implicative BCK-algebra is given. Following this, we prove that the adjoint semigroup of a general implicative BCK-algebra is an upper semilattice, and the adjoint semigroup of an implicative BCK-algebra with condition(s) is a distributive lattice. Finally, we prove the adjoint semigroup of a bounded implicative BCK-algebra is a Boolean algebra.
Keywords :
Boolean algebra; group theory; lattice theory; Boolean algebra; adjoint semigroup; distributive lattice; general implicative BCK-algebra; logical algebras; Boolean algebra; Educational institutions; Lattices; Moon; Nickel; System-on-a-chip;
Conference_Titel :
Fuzzy Systems and Knowledge Discovery (FSKD), 2011 Eighth International Conference on
Conference_Location :
Shanghai
Print_ISBN :
978-1-61284-180-9
DOI :
10.1109/FSKD.2011.6019493
