The Substructure Of Quantale And It's Properties

In this thesis,the author discusses the substructures of quantale and the properties of them.The author studies the relations among the quotient,subquantale and congruence classes by application of the nuclei conuclei and congruence.The author considers some special quantales and obtains some significant results.This thesis is consists of five chapters.In chapter one ,some recalled earlier results and three main areas of applications on the field of quantales are presented.Some main problems which will be searched arc interpreted.In chapter two, some basic operation and important results which will be necessary in next chapters.Some new properties of the operation are obtained.Some important characterization of prequantale are disscussed.The thired chapter summarizes the theme of algebraic nuclei mapping and conuclei mapping in original sense.Some interesting nuclei mapping and conuclei mapping are constructed.After characterization of nuclei and conuclei ,the quotient quantale and subquantale are explored and the equivalent condition of S- prime is achieved.The fourth chapter contains an extension for congruence of quantale by which the author discusses the inner structures of quantale.The equivalent conditions of congruence and semi-congruence are obtained and the simple quantale is explored by the congruence.The fifth chapter comes back to the characterization of Girard quantale,the sufficent and necessary conditions are proved on constructing the completely Boolean algebra from quantales.For all quotient Q_j of Girard quantale,its nuclei are found. For all subquantale of Girard quantale ,a sufficent condition which the subquantale becomes Girard quantale is obtained.For some logic operations,the algebraic operation of logic are explored.For each of involutive quantale,the algebraic structure and subquantale are discussed.