Sheaves of Paragraded Rings

In this paper we deal with sheaves of the category of paragraded rings with the same set of grades Δ, in short, the category of paragraded rings of type Δ, denoted by RP_Δ. The definition of a sheaf of category RP_Δ is the same as for any other category, but we are interested in the paragraded structure sheaf, as we named it here, and so, in some way we introduce the theory of paragraded structures into algebraic geometry. For this purpose we need to deal with homogeneous ideals, particularly, we need to introduce the prime spectrum of R(RP_Δ) and to analyze the localization of R. 2010 Mathematics Subject Classification. 16S60, 16S85, 16W99