| 质环的导子和同态 |
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| 引用本文： | 陈勇.质环的导子和同态[J].西南师范大学学报(自然科学版),1990,15(2):163-169. |
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| 作者姓名： | 陈勇 |
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| 作者单位： | 西南师范大学数学系 |
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| 基金项目： | 西南师范大学自然科学基金资助课题 |
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| 摘 要： | 为讨论环的交换性,本文讨论了导子成为同态或反同态时,环R的结构;证明了:定理1 R是一个质环,d是R的一个导子且为环R的同态,则d=0.定理2 R是一个质环,d是R的一个导子且为环R的反同态,则d=0.定理3 半质环R若满足下述条件则必为交换环(xy-yx)~2=xy~2-y~2x (?)~x,y∈R
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| 关 键 词： | 质环 导子 同态 反同态 交换性 |
DERIVATIONS AND HOMOMORPHISMS IN PRIME RINGS |
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| Chen Yong.DERIVATIONS AND HOMOMORPHISMS IN PRIME RINGS[J].Journal of Southwest China Normal University(Natural Science),1990,15(2):163-169. |
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| Authors: | Chen Yong |
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| Institution: | Southwest China Teachers University |
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| Abstract: | It is well-known that structure of a ring is very, tightly determined by the imposition of special behavior on one of its derivations. The following is proved with independent interest on the commutativity of rings.Theorem 1 Let R be a prime ring and d a derivation of R then d=0.Theorem 2 Let R be a prime ring arid d a derivation of R such that d is an anti-homomorphism of R, then d=0.Theorem 3 Let R be a semi-prime ring> then R is commutative if: |
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| Keywords: | prime ring derivation homomorphism anti-homomorphism commutativity |
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