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| Lie Homomorphism on the Associative Ring |
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Citation： |
Zhu Yuansen.Lie Homomorphism on the Associative Ring[J].Chinese Annals of Mathematics B,1982,3(6):813~818 |
| Page view： 836
Net amount： 980 |
Authors： |
Zhu Yuansen; |
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| Abstract： |
Is it true tliat Lie homomorpHisin (isomorphism) \phi of a ring R into a ring R' is
a homomorphism (isomorpliism) ? Herstein,I. N. and Kleinfeld, E. and Martindal, W. S.. obtained some results for simple ring and primitive ring,.
In this paper I shall study the Lie homomorphism on the associative ring and arrive at the following main conclusion:
Theorem. Suppose that R,R' are both associative rings with 1,and the center ofR’ does not contain zero divisor, where R’ is not of oharaoteristio 2 or 3. If \phi is a 3-Lie homomorphism of R onto R',then \phi must be either a homoinorpiiisin or the negative of an anti-homomorphism of R onto R'.
Theorem. Suppose that R is an associatiye ring and $R'\ne {0}$ is a prime ring,where (R', +) does not contain elements of the period 2 or 3. If \phi is a 3-Lie homomorphism of R onto R',then \phi it either a homomorphism or the negative of an antihomomorpliism of R onto R'.
Theorem. Suppose that R is an associative ring and (R, +) does not contain element of the period 2 or 3,R' is a prime ring. If \phi is a 3-Lie isomorpJlism of R onto R'。then \phi is either a isomorphism or the negative of an anti-isomorphism of R onto R'. |
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