Researches On Monoidal Lattice, Autonomous Poset And Convergence Of The Composition Of Quantale Matrices

The concept of quantale was introduced by C. J. Mulvey in 1986 with the purpose of studying the constructive foundations for quantum mechanics. It is very important of quantale in the researches of non-commutative C*-algebra, the theory of ring and the spectral of ring, the theory of Topos, which greatly advances the development of the theory of quantale. There are abundant contents in the struture of quantale, because quantale can be regarded as the generalization of frame.This paper mainly analyses and studies some properties of the ideal and spectral of monoidal lattice. Moreover, some researches about the ideals and the radical of ideals of autonomous poset have been done.Besides, we also have obtained some results about quantale matrix.The main content is as follows:In Chapter 1, Preliminary knowledge. In this chapter, we give the basic concepts and results of the theory of lattice and the theory of quantale which are used in the whole paper.In Chapter 2, Involutive monoidal lattice. In the first part of this chaper, the author gives the concept of involutive monoidal lattice, then obtains the separation lemma of involutive monoidal lattice by using the theory of prime ideal theory of general algebra. In the second part of this chaper, we discuss the theory of spectral of involutive monoidal lattice and some results are obtained. At last, we study the maximal ideal space of involutive monoidal lattice.In Chapter 3, Ideal of autonomous poset. Firstly, the concept of ideal of autonomous poset is given and some character theories are obtained. Secondly, we study the properties of operation on ideal of autonomous poset. Thirdly, we obtain some results about ideal, prime ideal and completely prime ideal of autonomous poset. At the same time, we also discuss the relations among them. At last, introducing the definition of radical of ideal of autonomous poset, we can get some properties of it.In Chapter 4, Convergence of the composition of quantale matrices. In the final chaper,we study the composition of & — V of quantale matrix and discuss the convergence of this composition of quantale matrix.