Rep(F[C_(2^(α))])的Krull维数与准素分解  

Krull dimension and primary decomposition of Rep(F[C_(2^(α))])

作　　者：卢鑫 唐国平 LU Xin;TANG Guoping(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报(中英文)》2025年第2期145-152,共8页Journal of University of Chinese Academy of Sciences

基　　金：国家自然科学基金(12271500)资助。

摘　　要：令F为特征为2的域,C_(2^(α))为2^(α)阶循环群。以群代数F[C_(2^(α))]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[C_(2^(α))]的表示环,记为Rep(F[C_(2^(α))]).在Higman工作的基础上进一步研究证明表示环Rep(F[C_(2^(α))])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[C_(2^(α))])是reduced环,并给出零理想的极小准素分解。最后证明Spec(Rep(F[C_(2^(α))]))是连通的拓扑空间。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.

关 键 词：表示环 素理想 模表示 

分 类 号：O153.3[理学—数学]