We investigate the formal matrix ring over defined by a certain system of factors. We give a method for constructing formal matrix rings from non-negative integer matrices. We also show that the principal factor matrix of a binary system of factors determine the structure of the system.
Let F: R → R/G be a Galois covering and (resp. ) be a full subcategory of the module category mod (R/G), consisting of all R/G-modules of first (resp. second) kind with respect to F. The structure of the categories and is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.
In this paper, complex 3-dimensional Γ-graded ε-skew-symmetric and complex 3-dimensional Γ-graded ε-Lie algebras with either 1-dimensional or zero homogeneous components are classified up to isomorphism.