| 广义幂级数上的GPP-环 |
| |
| 引用本文： | 杨晓燕.广义幂级数上的GPP-环[J].河西学院学报,2004,20(5):7-10. |
| |
| 作者姓名： | 杨晓燕 |
| |
| 作者单位： | 西北师范大学数学与信息科学学院,甘肃,兰州,730070 |
| |
| 摘 要： | 设R是交换环,(S,≤)是严格全序幺半群.本文证明了:(1)广义幂级数环RS,≤]]是强GPP-环当且仅当R是强GPP-环,且B(R)(R的所有幂等元的集合)的任意S-加标子集C在B(R)中有最小下界.(2)如果(S,≤)满足条件:任意S∈S,s≥0,则环RS,≤]]是弱GPP-环当且仅当R是弱GPP-环.
|
| 关 键 词： | 广义幂级数环 强GPP-环 弱GPP-环 |
GPP-rings of generalized power series |
| |
| YANG Xiao-yan.GPP-rings of generalized power series[J].Journal of Hexi University,2004,20(5):7-10. |
| |
| Authors: | YANG Xiao-yan |
| |
| Institution: | Northwest Normal University Department of Mathematics Gansu Lanzhou 730070 |
| |
| Abstract: | Let be a commutative ring and a strictly totally ordered monoid.In this paper we prove that the ring ]] of generalized power series is a strongly ring if and only if is a strongly ring and every -indexed subset of (the set of all idempotents of )has a least upper bound in ,and if also satisfied the condition that for any .then the ring ]] is weakly ring if and only if is weakly ring. |
| |
| Keywords: | ring of generalized power series strongly ring weakly ring |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
