| 偏序集的关联环的同构问题 |
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| 引用本文： | 朱彬.偏序集的关联环的同构问题[J].数学学报,1997,40(3):423-428. |
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| 作者姓名： | 朱彬 |
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| 作者单位： | 北京师范大学数学系 |
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| 摘 要： | 设Ｘ是局部有限偏序集（或拟序集），Ｒ是含１的结合环，Ⅰ（Ｘ，Ｒ）是Ｒ上Ｘ的关联环，关联环的同构问题是指：问题１：怎样的环，能使环同构Ⅰ（Ｘ，Ｒ）Ⅰ（Ｘ，Ｒ）推出偏序集之间的同构Ｘ芒Ｘ’？问题２：怎样的环或偏序集，能使环同构Ⅰ（Ｘ，Ｒ）Ⅰ（Ｘ，Ｓ）推出Ｒ Ｓ？本文证明了对唯一幂等元环（非交换），问题１有正面回答；对问题２，我们证明了对交换不可分解环Ｒ、Ｓ，由环同构Ⅰ（Ｘ，Ｒ）Ⅰ（Ｘ，Ｒ）可得到Ｒ＝Ｓ，Ｘ＝Ｘ’。
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| 关 键 词： | 关联环，偏序集，同构问题 |
| 收稿时间： | 1995-11-22 |
The Isomorpbism Problems for Incidence Riags of Partially Ordered Sets |
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| Zhu Bin.The Isomorpbism Problems for Incidence Riags of Partially Ordered Sets[J].Acta Mathematica Sinica,1997,40(3):423-428. |
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| Authors: | Zhu Bin |
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| Institution: | Zhu Bin (Department of Mathematis, Beijing Normal Universty, Beijing 1 00875 , China) |
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| Abstract: | Let . be a locally finite partially ordered set, R is an ring with identity 1, I(x, R) is the incidence ring of X over R, the isomorphism problems about incideace riags are discussed in the present paper. The following results are obtained : If R is an unique idempotent ring, the. ordered sets) : If R,S. are commutative iadecomposable riogs, then |
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| Keywords: | Incidence riaga Partially ordered set Isomorpbism pmblems |
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