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.
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.
基金
National Natural Science Foundation of China (Grant No. 11171240)
Fundamental Research Funds for the Central Universities,Southwest University for Nationalities (Grant No. 11NZYQN24)
