Prime spectra of additive categories (I) Original Research Article

In this paper, by introducing appropriate notions of multiplication of ideals (resp. sieves) of an additive category C, we associate to the category a topological space Spec(C) consisting of all globally prime ideals. We can also associate to each object C Σ C a space Spec(C) consisting of all prime 2-sided sieves at C in such a way that each local spectrum Spec(C) is a retract of the global spectrum Spec(C).