Strongly Maximal Taf Algebras D-mode

Strongly maximal TAF algebras is a class of important non-selfadjoint operatoralgebras, whose D-modules are the basic elements of the algebraic structure, so thestudy of the D-modules in Strongly maximal TAF algebras is meaningful. This thesis ismainly concerned with the properties of D-modules in Strongly maximal TAF algebras.In Chapter 1, the background and some preliminary are introduced.In Chapter 2, the concrete form of meet irreducible D-modules in full up triangularmatrix algebras is studied, and it provides the concrete model and background for thefollowing sections.In Chapter 3, we construct a D-module in Strongly maximal TAF algebras, andprove that it is meet irreducible.In Chapter 4, we construct a chain of matrix units in Strongly maximal TAFalgebras, and prove that the corresponded D-module to the chain is meet irreducible.In Chapter 5, we consider completely meet irreducible D-modules in Stronglymaximal TAF algebras, and prove that every completely meet irreducible D-modulecorresponds to a CMD-chain.