正合零因子下模的Gorenstein同调维数
Gorenstein homological dimensions of modules under exact zero-divisors

摘要： 设R是具有单位元的交换Noether环,x是R上的正合零因子。研究了正合零因子下模的Gorenstein同调维数,证明了若M是Gorenstein投射(内射,平坦)R-模,则M/xM是Gorenstein投射(内射,平坦)R/xR-模,得到了有关维数的结论。对Ding投射(内射)R-模可得类似的结论。
Abstract: Let R be a commutative Noetherian ring with identity, x be an exact zero-divisor over R. Gorenstein homological dimensions of modules under exact zero-divisors are investigated. M/xM is Gorenstein projective(injective, flat)R/xR-module if M is Gorenstein projective(injective, flat)R-module, the results of corresponding dimensions are gained. The result can also be obtained for Ding projective(injective)R- modules