绝对不可约F[H]-模的扩充

journal6 ›› 2003, Vol. 24 ›› Issue (4): 82-83.

绝对不可约F[H]-模的扩充

(吉首大学数学与计算机科学系，湖南吉首 416000)

出版日期:2003-12-15 发布日期:2012-11-06
作者简介:杨玉英(1970-)，女，湖南省靖州县人，硕士，吉首大学数学与计算机科学系讲师，主要从事代数学研究.

The Extension of Absolutely Irreducible F[H]-Module

(Dept. of Math. and Computer Science,Jishou University,Jishou 416000,Hunan China)

Online:2003-12-15 Published:2012-11-06

摘要/Abstract

摘要：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.

关键词： 代数闭域, 绝对不可约F[H]-模, 扩充

Abstract: The topic of this paper is the discussion about the extension of absolutely irreducible F[H]-module,and the author obtains the sufficient condition's extension:if there exists a∈F,and an=σｎ，Ｎ can be extended into F[G]-module.

Key words: algebric round field, absolutely irreducible F[H]-module, extension

杨玉英. 绝对不可约F[H]-模的扩充[J]. journal6, 2003, 24(4): 82-83.

YANG Yu-Ying. The Extension of Absolutely Irreducible F[H]-Module[J]. journal6, 2003, 24(4): 82-83.