absolutely irreducible variety

The topic of this paper is the discussion about the extension of absolutely irreducible F-module,and the author obtains the sufficient condition s extension:if there exists a∈F,and a~n=σ_n,N can be extended into F-module.

设N为绝对不可约F[H]-模,T(N)=G,G/H是n阶循环群,H\G={gi｜i=0,1,…,n-1};g∈G,gn∈H,φ为N的Q-自同构,σn:xφn(x)gn=φn(x)h0,经讨论,获得绝对不可约F[H]-模的扩充存在的充分条件是若存在a∈F(F为任意域),使an=σn,则N可扩充为F[G]-模;若G为交换群,F为代数闭域, H≤G,N为任意不可约F[H]-模N,则N可扩充为F[G]-模。