关于高等代数中命题的反例研究  

Research of counter-example about proposition in higher algebra

作　　者：杨侠[1] 孙自行[1] 

机构地区：[1]阜阳师范学院数学与计算科学学院,安徽阜阳236000

出　　处：《阜阳师范学院学报（自然科学版）》2010年第4期35-37,共3页Journal of Fuyang Normal University(Natural Science)

基　　金：阜阳师范学院校级青年项目(2008JQ09)资助

摘　　要：反例在高等代数命题研究中有着独特的作用,然而,在高等代数教学及理论研究中,人们往往忽视了反例的效用。通过综合论述高等代数中命题的反例,对高等代数中若干命题通过消弱命题条件或变换命题条件和结论进行研究,得出了关于向量组、矩阵、线性变换、多项式等方面的命题的反例,深入探讨了关于多项式的不可约性、子空间的直和判定及矩阵相似性三方面的命题,从而深化了对原命题的理解和认识。高等代数中命题的反例研究有利于提高批判性思维和创造性思维能力,有利于提高对命题的深层次理解,对于高等代数教学及理论研究均有一定的指导意义。Counter-example in the study of advanced algebra proposition has a unique role,however,in theory research and teaching,people often overlook the effectiveness of counter-example.By weakening conditions of proposition or changing the conditions and conclusions,counter-examples in the advanced algebra is discussed and counter-example of propositions on the vector group,matrix,linear transformation and polynomial is obtained,and propositions on the irreducibility of polynomials,determination of direct sum about sub-space and matrix similarity is further studied,thereby deepening the understanding and knowledge of the original proposition.In higher algebra the study of propositions＇ counter-example improves critical thinking and creative thinking,improves understanding of the underlying proposition and has a certain significance for higher algebra teaching and theory.

关 键 词：高等代数 命题 反例研究 

分 类 号：O175[理学—数学]