| 可除酉D模的构造 |
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| 引用本文： | 孙继逊.可除酉D模的构造[J].湖北大学学报(自然科学版),1990(1). |
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| 作者姓名： | 孙继逊 |
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| 作者单位： | 湖北大学数学系 |
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| 摘 要： | 本文构造了可除模K/D及其子模D(p~∞),得到以下结果:(1)如果可除酉D模是挠的,则它同构于D(p~∞)的多重直和;(2)如果可除酉D模是挠自由的,则它同构于K的多重直和;(3)每个可除酉D模同构于多重K与多重D(p~∞)的直和(p是变动的)。
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| 关 键 词： | 欧几里得整环 主整理想 阶理想 挠模 挠自由模 可除模 内射模 |
THE STRUCTURE OF DIVISIBLE UNITARY D-MODULES |
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| Sun Jixun.THE STRUCTURE OF DIVISIBLE UNITARY D-MODULES[J].Journal of Hubei University(Natural Science Edition),1990(1). |
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| Authors: | Sun Jixun |
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| Institution: | Department of Mathematics |
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| Abstract: | The notion of divisible module is quoted in this article. It points out that K/D is a divisible unitary D-module and obtains the following results; (1) If a divisible unitary D/module is torsional, then it is isomorphic to a direct sum of copies of D(p). (2) If a divisible unitary D-module is torsion-free, then it is isomorphic to a direct sum of copies of K. (3) Every divisible unitary D-module is isomorphic to a direct sum of copies of K and copies of D(p) for various primes P in D. |
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| Keywords: | Euclidian domain Principle ideal domain Orderiddal Torsion module Torsion- free module Divisible module Injective module |
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