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Central *-Differential Identities in Prime Rings

Published online by Cambridge University Press:  20 November 2018

P. H. Lee  and
T. L. Wong
P. H. Lee
Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan
T. L. Wong
Affiliation:
Department of Mathematics, National Taiwan University, Taipei, Taiwan
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Abstract

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Let R be a prime ring with involution and d, δ be derivations on R. Suppose that xd(x)—δ(x)x is central for all symmetric x or for all skew x. Then d = δ = 0 unless R is a commutative integral domain or an order of a 4-dimensional central simple algebra.

Keywords

16W2516W1016N6016R50involutionderivationsymmetric elementskew element
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 2 , 01 June 1996 , pp. 211 - 215
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Bresar, M., Centralizing mappings and derivations in prime rings, J. Algebra 156(1993), 385—394.Google Scholar
2. Chuang, C. L., *-differential identities of prime rings with involution, Trans. Amer. Math. Soc. 316(1989), 251–279.Google Scholar
3. Erickson, T. S., Martindale, W. S. and Osborn, J. M., Prime nonassociative algebras, Pacific J. Math. 60 (1975), 49–63.Google Scholar
4. Herstein, I. N., Rings with Involution, Univ. Chicago Press, Chicago, 1976.Google Scholar
5. Herstein, I. N., A note on derivations II, Canad. Math. Bull. 22( 1979), 509–511.Google Scholar
6. Herstein, I. N., A theorem on derivations of prime rings with involution, Canad. J. Math. 34(1982), 356–369.Google Scholar
7. Lee, P. H. and Lee, T. K., Derivations centralizing symmetric or skew elements, Bull. Inst. Math. Acad. Sinica 14(1986), 244–256.Google Scholar
8. Lin, J. S., On derivations of prime rings with involution, Chinese J.Math. 14(1986), 37—51.Google Scholar
9. Martindale, W. S., Prime rings satisfying a generalized polynomial identity, J.Algebra 12(1969), 576–584.Google Scholar