Congruence and nucleus of double quantale module
Shao Liang · Journal of Sichuan University · 2011
In this paper the definition of double quantale module is given,some properties of double quantale module are discussed.The author present the concepts of congruence and nucleus of double quantale module,and study some properties of them,and prove that the surjective homomorphisic image of a double quantale module is isomorphic to the image of some double quantale module nucleus.Then a one-to-one correspondence between the set of all double quantale module nuclei on an double quantale module and the set of all the congruence relations on it can be obtained.They are isomorphic complete lattices.