by Li Ho-chun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 97-100). / Introduction --- p.iv / Chapter 1 --- Spectral spaces --- p.1 / Chapter 1.1 --- Basic notions --- p.1 / Chapter 1.1.1 --- Order compatible topology --- p.1 / Chapter 1.1.2 --- Prime spectrums and Zariski topology --- p.3 / Chapter 1.1.3 --- Lattice-ordered groups --- p.4 / Chapter 1.1.4 --- Spectral spaces and patch topology --- p.5 / Chapter 1.2 --- Properties of patches and the patch topology --- p.6 / Chapter 1.3 --- Properties of spectral spaces --- p.8 / Chapter 1.4 --- Another characterization of spectral spaces --- p.13 / Chapter 1.5 --- The maxspectral spaces --- p.14 / Chapter 2 --- The ordering on Spec(R) --- p.16 / Chapter 2.1 --- Two distinguished properties of a spectral poset --- p.17 / Chapter 2.2 --- Finite partially ordered sets --- p.18 / Chapter 2.3 --- Several classes of special rings --- p.19 / Chapter 2.4 --- Spectral trees --- p.23 / Chapter 2.5 --- Ordered disjoint unions --- p.26 / Chapter 2.6 --- Another necessary condition for a poset to be spectral --- p.31 / Chapter 2.7 --- Possible partial orderings for spectral posets --- p.33 / Chapter 3 --- The topology on Spec(R) --- p.35 / Chapter 3.1 --- Basic notions about Spec(R) --- p.35 / Chapter 3.2 --- The Zariski topology on Spec(R) --- p.37 / Chapter 3.2.1 --- Hausdorffness --- p.37 / Chapter 3.2.2 --- Irreducibility --- p.41 / Chapter 3.2.3 --- Connectedness --- p.45 / Chapter 3.2.4 --- Normality --- p.49 / Chapter 3.3 --- Topology on Min(R) and Baer rings --- p.55 / Chapter 4 --- Study algebraic properties from Spec(R) --- p.68 / Chapter 4.1 --- Prime spectrums of Bezout rings --- p.69 / Chapter 4.2 --- D-closed subsets of Spec(R) --- p.84 / Chapter 4.3 --- The C(m) topology --- p.88 / Chapter 4.4 --- Prime spectrum of Noetherian ring --- p.89 / Chapter 4.5 --- Reduced Bezout rings that are coherent --- p.93 / Chapter 4.6 --- Applications --- p.94 / Bibliography --- p.97