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一类广义幂级数环的有限维数

Keywords: 代数,,广幂级数环,有限维数

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Abstract:

令R是一个有单位元的完备的凝聚交换环,研究并比较了R的有限维数与R上的广义幂级数环R≤,S的有限维数的关系,得到了一些有限维数不等式.结果表明:如果R是一个完备的凝聚的有单位元的交换环,则R的有限投射维数不超过RS,≤的有限投射维数;令R是一个完备的凝聚的有单位元的交换环,则R的有限内射维数不超过RS,≤的有限内射维数;如果R是一个完备的凝聚的有单位元的交换环,则R的有限弱维数不超过RS,≤的有限弱维数.

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