No abstract

Abstract. Consider an (associative) matrix algebra M I (R) graded by means of an abelian group G, and a graded automorphism φ on M I (R). By defining a new product by x ⋆ y := φ(x)φ(y) on M I (R), (M I (R), ⋆) becomes a hom-associative algebra graded by a twist of G. The structure of (M I (R), ⋆) is studied, by showing that M I (R) is of the formwith U an R-submodule of the 0-homogeneous component and any I j a well described graded ideal of M I (R), satisfying I j ⋆ I k = 0 if j = k. Under certain conditions, the graded simplicity of an arbitrary graded hom-associative algebra M is characterized and it is shown that M is the direct sum of the family of its simple graded ideals.