令F为特征为2的域，C2α为2α阶循环群。以群代数F[C2α]的所有有限维不可分解模的同构类为Z-基，以F模的张量积为乘法所构成的环称为F[C2α]的表示环，记为Rep(F[C2α]). 在Higman工作的基础上进一步研究证明表示环Rep(F[C2α])的Krull维数1并得到其所有素理想的具体形式。之后证明Rep(F[C2α])是reduced环，并给出零理想的极小准素分解。最后证明Spec(Rep(F[C2α]))是连通的拓扑空间。
Let F be a field with characteristic 2 and C2α be a cyclic group with order 2α. The ring, which has a Z-basis by finite dimensional indecomposable F[C2α] modules and multiplications by tensor product of F module, is called representation ring and denoted by Rep(F[C2α]). Based on Higman’s work, we further get the Krull dimension and the concrete forms of all prime ideals of Rep(F[C2α]). And then, we prove that Rep(F[C2α]) is a reduced ring and find the minimal primary decomposition of the zero ideal. At last, we prove that Spec(Rep(F[C2α])) is a connected topological space.
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