I type structure on a Quantale and its properties

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.