半自反根与半自反模

On semi-reflexive radicals and semi-reflexive modules

从不同角度引入半自反模和半自反维数的概念 ,并根据半自反维数的特性 ,讨论了环的分类 ,给出了半自反维数为 0和 1的两类环的存在性以及GN -环上的有限生成半自反模的结构 ,即他是有限生成自由模的子模 .借助亚投射性和半自反性的关系 ,详细讨论了投射根P (R) =0的交换环R上的半自反模的一些性质 .

In this paper,we introduce semi-reflexive module by means of semi-reflexive radical,and introduce semi-reflexive dimension of module in terms of meta-projectivity.The classification of rings is studied,the existences of rings with semi-reflexive dimension zero or one are discussed.The structures of finitely generated semi-reflexive modules over GN-ring are obtained.Based on relations between meta-projectivity and semi-reflexivity,some properties of semi-reflexive modules over a commutative ring R with P(R)=0 are characterized.