Abstract:
The concepts of an I type structure and a weak substructure on a Quantale are introduced, the corresponding relations between I type structures (weak structures) and maps are discussed. By using the operations , ∨ and ∧ of a Quantale, sufficient and necessary conditions for a nonempty subset to be an I type ideal and a weak subquantale are given, respectively. Finally, it is proved that I type nuclei and I type ideal conuclei are in one-to-one correspondence on pre-Girard Quantale.
