| 关于Monogeny和Epigeny模类 |
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| 引用本文： | 刘仲奎.关于Monogeny和Epigeny模类[J].数学研究及应用,2004,24(4):589-596. |
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| 作者姓名： | 刘仲奎 |
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| 作者单位： | 西北师范大学数学系,甘肃,兰州,730070 |
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| 基金项目： | SupportedbyNationalNaturalScienceFoundationofChina(10171082)
theTeachingandResearchAwardProgramforOutstandingYoungTeachersinHigherEducationInstitutionsofMOE,P.R.C. |
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| 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).
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| 关 键 词： | Monogeny类 Epigeny类 广义幂级数环 |
| 收稿时间： | 2002/10/16 0:00:00 |
On Monogeny and Epigeny Classes of Modules |
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| LIU Zhong-kui.On Monogeny and Epigeny Classes of Modules[J].Journal of Mathematical Research with Applications,2004,24(4):589-596. |
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| Authors: | LIU Zhong-kui |
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| Institution: | Dept. of Math.; Northwest Normal University; Lanzhou; China |
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| Abstract: | Let (S, ≤) be a strictly totally ordered monoid, and M and N be left Rmodules. 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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| Keywords: | Monogeny class Epigeny class generalized power series ring |
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