Nagata-like theorems for almost Prüfer v-multiplication domains |
| |
作者姓名: | LI Qing |
| |
作者单位: | College of Computer Science and Technology,Southwest University for Nationalities |
| |
基金项目: | National Natural Science Foundation of China (Grant No. 11171240);Fundamental Research Funds for the Central Universities,Southwest University for Nationalities (Grant No. 11NZYQN24) |
| |
摘 要: | Let D be an integral domain and X an indeterminate over D . We show that if S is an almost splitting set of an integral domain D , then D is an APVMD if and only if both DS and DN(S) are APVMDs. We also prove that if {Dα}α∈I is a collection of quotient rings of D such that D=∩α∈IDα has finite character (that is, each nonzero d∈D is a unit in almost all Dα) and each of Dα is an APVMD, then D is an APVMD. Using these results, we give several Nagata-like theorems for APVMDs.
|
关 键 词: | splitting set Nagata-like theorem almost Prfer v-multiplication domain |
本文献已被 CNKI SpringerLink 等数据库收录! |