| 有限交换幺环的自同态 |
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| 引用本文： | 朱用文.有限交换幺环的自同态[J].烟台大学学报(自然科学与工程版),2001,14(1):11-14. |
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| 作者姓名： | 朱用文 |
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| 作者单位： | 烟台大学 数学与信息科学系，山东 烟台 264005 |
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| 摘 要： | Pramod K．Sharma and S．M，Bhatwadekar给出了有限交换幺环的色数公式，在此基础上研究环图的同态，得到了关于有限交换幺环的一系列优美结果，如：有限交换幺环在保幺自同态下的像环与原环具有相同的色数、融数和单位元集，有限半单交换幺环的保幺自同态必为自同构，等等。
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| 关 键 词： | 环 图 同态 色数 融数 |
| 文章编号： | 1004-8820(2001)01-0011-04 |
Endomorphisms of a Finite
Commutative Ring with Identity |
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| ZHU Yong-wen.Endomorphisms of a Finite
Commutative Ring with Identity[J].Journal of Yantai University(Natural Science and Engineering edirion),2001,14(1):11-14. |
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| Authors: | ZHU Yong-wen |
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| Abstract: | The enumeration of chromatic number for a finite commutative ring with identity was given by Pramod Sharma and Bhatwadekar. In this paper, this kind of rings is researched further by the means of homomorphisms of the ring's graphs. A series of graceful results are obtained: an endomorphism of a finite commutative ring with identity must preserve the chromatic number, the clique number and the units' set if it preserves the identity. Moreover, it would be an automorphism of the ring when the ring is semisimple, etc. |
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| Keywords: | ring graph homomorphism chromatic number clique number |
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