| 相对半遗传环与半遗传环 |
| |
| 引用本文： | 班秀和.相对半遗传环与半遗传环[J].湖南文理学院学报(自然科学版),2007,19(4):25-26. |
| |
| 作者姓名： | 班秀和 |
| |
| 作者单位： | 广西师范学院,数学与计算机科学系,广西,南宁,530001 |
| |
| 基金项目： | 广西科学基金(0575052，0640070) |
| |
| 摘 要： | 用余平坦模和M-半遗传环刻画了半遗传环,得到:R是半遗传环,当且仅当E(R)的商是余平坦模,当且仅当R是R-半遗传环,当且仅当每个模的任意两个同构内射子模的和是余平坦模.还用余平坦模刻画了QF-环和正则环,证明了:R为QF-环,当且仅当余平坦模是投射模,当且仅当投射模是余平坦模且R是Noether环;R为正则环当且仅当R的每个循环左理想余平坦.
|
| 关 键 词： | 余平坦模 M-半遗传环 半遗传环 QF-环 正则环 |
| 文章编号： | 1672-6146(2007)04-0025-02 |
| 修稿时间： | 2007年8月10日 |
Relative Semi-hereditary Rings and Semi-hereditary Rings |
| |
| BAN Xiu-he.Relative Semi-hereditary Rings and Semi-hereditary Rings[J].Journal of Hunan University of Arts and Science:Natural Science Edition,2007,19(4):25-26. |
| |
| Authors: | BAN Xiu-he |
| |
| Abstract: | Using coflat modules and M-semi-hereditary rings, it is obtained that R is a semi- hereditary ring iff the factors of E(R) is coflat iff R is a R-semi-hereditary ring iff the sum of two injective submodules in a module that are isomorphic is coflat.Then, by coflat modules the following results are shown: R is a QF- ring iff coflat modules are projective iff projective modules are coflat and R is a Noetherian ring;R is a regular ring iff every cyclic left ideal in R is coflat. |
| |
| Keywords: | coflat module M-semi-hereditary ring semi-here-ditary ring QF- ring regular ring |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
