Abstract: Let F be a field with characteristic 2 and C_2^α be a cyclic group with order 2^α. The ring, which has a Z-basis by finite dimensional indecomposable F[C_2^α] modules and multiplications by tensor product of F module, is called representation ring and denoted by Rep(F[C_2^α]). Based on Higman’s work, we further get the Krull dimension and the concrete forms of all prime ideals of Rep(F[C_2^α]). And then, we prove that Rep(F[C_2^α]) is a reduced ring and find the minimal primary decomposition of the zero ideal. At last, we prove that Spec(Rep(F[C_2^α])) is a connected topological space.

Key words: representation ring, prime ideal, modular representation