| 2型X—extending模与Osofsky—smith定理 |
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| 引用本文： | 何万生.2型X—extending模与Osofsky—smith定理[J].数学理论与应用,2002,22(2):20-22,11. |
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| 作者姓名： | 何万生 |
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| 作者单位： | 天水师范学院数学系，天水741001 |
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| 摘 要： | 设R是有单位元的环，X是所有半单左R一模及Singular左R－模构成的模类，M是循环的extending左R一模，本文证明了若M的所有循环子商都是2型X－extending模，则M具有有限一致维数，该结果推广了著名的Osofsky-Smith定理。
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| 关 键 词： | 2型X－extending模 Osofsky－Smith定理 有限一致维数 环 循环子商 |
Type 2 X-extending modules and Osofsky-Smith Theorem |
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| He Wansheng.Type 2 X-extending modules and Osofsky-Smith Theorem[J].Mathematical Theory and Applications,2002,22(2):20-22,11. |
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| Authors: | He Wansheng |
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| Abstract: | Let R be a ring with identity,and X be the module class consists of all semisimple and all singular left R-modules.For a cyclic extending left R-module M,we show that if all cyclic subfactors of M are type 2 X-extending,then M has finite uniform dimension.This result is a generalization of Osofsky-Smith Theorem. |
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| Keywords: | extending module type 2 X-extending module finite uniform dimension |
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