| 刘仲奎.关于Monogeny和Epigeny模类(英文)[J].数学研究及应用,2004,24(4):589~596 |
| 关于Monogeny和Epigeny模类(英文) |
| On Monogeny and Epigeny Classes of Modules |
| 投稿时间：2002-10-16 |
| DOI：10.3770/j.issn:1000-341X.2004.04.003 |
| 中文关键词: Monogeny类 Epigeny类 广义幂级数环 |
| 英文关键词:Monogeny class Epigeny class generalized power series ring |
| 基金项目: |
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| 摘要点击次数: 2760 |
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| 中文摘要: |
| 设(S,≤)是严格全序幺半群,M和N是左R-模。记A=[[RS,≤]]。证明了如下结论:(1)如果(S,≤)是有限生成的且对任意s∈S有0≤s,则Epi([[RS,≤]][[MS,≤]]) = Epi([[RS,≤]][[NS,≤]])当且仅当Epi(M)=Epi(N);(2)如果(S,≤)是Artinianr ,则 Mono([[RS,≤]][MS,≤])= Mono([[RS,≤]][NS,≤])当且仅当Mono(M)=Mono(N). |
| 英文摘要: |
| Let (S, ≤) be a strictly totally ordered monoid, and M and N be left R modules. We show the following results: (1) If (S, ≤) is finitely generated and satisfies the condition that 0≤S for any s ∈S, then Epi([[RS,≤]][[MS,≤]]) = Epi([[RS,≤]][[NS,≤]]) if and only if Epi(M) = Epi(N); (2) If (S,≤) is artinian, then Mono([[RS,≤]][MS,≤])= Mono([[RS,≤]][NS,≤]) if and only if Mono(M) = Mono(N). |
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