1. This is an indecomposable substance.

2. In addition, a characterization of hereditarily indecomposable Banach spaces is given in terms of the properties of the extension of minimal sequences.

3. The concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice L are introduced, and some algebraic properties of them are obtained.

4. In this paper, we construct a class of indecomposable solvable Lie algebras of dimension 5 with the simplest filiform nilradicals over complex field.

5. Secondly, we discuss the problem of decomposing a nonnegative matrix into a product of fully indecomposable nonnegative matrices in chapter 2.

6. In this paper we systematically analyse and generalize the Boson Realization Method proposed by the author for constructing indecomposable representations of Lie (super) algebras.