余剩余格的理想和嵌入定理

Ideals and embedding theorem of co-residuated lattices

基于余剩余格理论,给出了余剩余格的理想、主理想、素理想、极大理想和同态的概念,讨论了它们的性质,并引入距离函数,给出了余剩余格中的同余关系.研究得到余剩余格的嵌入定理,即满足预线性条件的余剩余格均可同构于一簇全序余剩余格乘积代数的子代数.

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.