环与代数中的Phantom理想及本质余挠包络

发布时间：2018-06-10 09:09

本文选题：phantom理想 + IF环　；参考：《东北师范大学》2017年硕士论文

【摘要】：本文首先讨论了环与代数中的phantom理想.我们证明了若两个群代数是稳定等价的,则它们具有相同的phantom数.作为应用,我们计算了两个群代数的phanto-m数的上界.我们的例子用这一方法可以极大的降低phantom数的上界.我们还证明了若环是IF的,则其上的phantom理想等于cophantom理想.然后,我们研究了每个右模都存在本质余挠包络的环.我们证明了环R的每个右R-模具有本质余挠包络当且仅当循环奇异平坦模范畴L是商下封闭的,且C是L的右正交类.作为应用,我们得到如下刻画:如果R是一个交换环,且每个右R-模具有本质余挠包络,那么此环一定是一个max环,也就是说,R/J(R)是一个冯诺依曼正则环,且J(R)是T-幂零的,其中J(R)是R的Jacobson根.
[Abstract]:This paper first discusses phantom ideals in ring and algebra. We prove that if two group algebras are stable equivalent, they have the same phantom number. As an application, we calculate the upper bounds of the phanto- m numbers of two group algebras. Our example can greatly reduce the upper bounds of the number of phantom. The ring is IF, then the phantom ideal on the ring is equal to the cophantom ideal. Then, we study the ring of the intrinsic redundancy envelope for each right mode. We prove that every right R- mold of the ring R has the essential residual envelope when and only if the cyclic singular flat model domain L is closed, and C is the right orthogonal class of L. As an application, we get the example Below: if R is an exchange ring, and every right R- die has an essential torsion envelope, then this ring must be a max ring, that is, R/J (R) is a Von Neumann regular ring, and J (R) is a T- power zero, and J (R) is a R Jacobson root.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O153.3

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