Algebraic view over homogeneous linear recurrent processes

In this paper the algebraic properties of the deterministic processes with dynamic represented by a homogeneous linear recurrence over the field $\mathbb{C}$ are studied. It is started with an overview of homogeneous linear recurrent processes over $\mathbb{C}$ and its subsets. Next, it is gone deeper into homogeneous linear recurrent processes over numerical rings. After that, the recurrence criteria over sign-based ring subsets are analyzed. Also, the deterministic processes with dynamic represented by a Littlewood, Newman or Borwein homogeneous linear recurrence are considered.