| 广义幂级数环的Morita对偶 |
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| 引用本文： | 刘仲奎.广义幂级数环的Morita对偶[J].数学学报,2005,48(2):397-402. |
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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 兰州730070 |
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| 基金项目： | 国家自然科学基金(10171082)
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| 摘 要： | 设A,B是有单位元的环, (S,≤)是有限生成的Artin的严格全序幺半群, AMB是双模.本文证明了双模AS,≤]]MS,≤]BS,≤]]定义一个Morita对偶当且仅当 AMB定义一个Morita对偶且A是左noether的,B是右noether的.因此A上的广 义幂级数环AS,≤]]具有Morita对偶当且仅当A是左noether的且具有由双模AMB 诱导的Morita对偶,使得B是右noether的.
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| 关 键 词： | Morita对偶 左线性紧模 广义幂级数环 |
Morita Duality for the Rings of Generalized Power Series |
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| Zhong Kui LIU.Morita Duality for the Rings of Generalized Power Series[J].Acta Mathematica Sinica,2005,48(2):397-402. |
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| Authors: | Zhong Kui LIU |
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| Institution: | Zhong Kui LIU Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China |
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| Abstract: | Let A, B be associative rings with identity, and (S,≤) a strictly totally ordered monoid which is also Artinian and finitely generated. For any bimodule AMB, we show that the bimodule AS,≤]]MS,≤]BS,≤]] defines a Morita duality if and only if AMB defines a Morita duality and A is left noetherian, B is right noetherian. As a corollary, it is shown that the ring AS,≤]] of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule AMB such that B is right noetherian. |
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| Keywords: | Morita duality Left linearly compact module Ring of generalized power series |
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