WANG Guo-jun1, ZHENG Mu-cong1, LIU Yan2
(1 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China; 2 Department of Basic Courses, Xi′an University of Science and Technology, Xi′an 710054, Shaanxi, China)
Abstract:
Based on the theory of co-residuated lattices,the concepts of ideal, principal ideal,prime ideal and maximal ideal of a co-residuated lattice are proposed and the properties of them are discussed.Then a distance function is introduced and a congruence on co-residuated lattices is given. Finally, an embedding theorem of co-residuated lattice is obtained, which states that a co-residuated lattice satisfying prelinear condition is isomorphic to a subdirect product of a chain of co-residuated lattices.
KeyWords:
co-residuated lattice; ideal; homomorphism; congruence; embedding theorem
