On automorphisms of prime rings with involution

L. A. Khan; A. B. Thaheem

doi:10.1515/dema-1997-0209

On automorphisms of prime rings with involution

L. A. Khan
, A. B. Thaheem

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

Original language	English
Pages (from-to)	307-311
Number of pages	5
Journal	Demonstratio Mathematica
Volume	30
Issue number	2
DOIs	https://doi.org/10.1515/dema-1997-0209
State	Published - Jan 1997

Bibliographical note

Funding Information:
Now assume that a(x) = axa-1 for all x € R, a 6 R. Then by assumption, a2xa~2 = a* xa* for all x £ R. This implies that a*a2x = xa*a2 or a'aax — xa'a a = 0 for all x € R. Since a*a € Z(R), therefore rewriting the preceding equation we get ama(ax — xa) = 0 for all x 6 R. Since a"a is not a zero divisor, therefore ax = xa for all x 6 R and hence a is a central element. This proves that a = 1. The converse is simple. This completes the proof. • Acknowledgements. The authors wish to thank the referee for valuable suggestions which helped to improve the paper. One of the authors (A.B. Thaheem) gratefully acknowledges the support provided by King Fahd University of Petroleum and Minerals during this research.

ASJC Scopus subject areas

General Mathematics

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10.1515/dema-1997-0209

Cite this

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title = "On automorphisms of prime rings with involution",

author = "Khan, \{L. A.\} and Thaheem, \{A. B.\}",

note = "Funding Information: Now assume that a(x) = axa-1 for all x € R, a 6 R. Then by assumption, a2xa\textasciitilde{}2 = a* xa* for all x £ R. This implies that a*a2x = xa*a2 or a'aax — xa'a a = 0 for all x € R. Since a*a € Z(R), therefore rewriting the preceding equation we get ama(ax — xa) = 0 for all x 6 R. Since a{"}a is not a zero divisor, therefore ax = xa for all x 6 R and hence a is a central element. This proves that a = 1. The converse is simple. This completes the proof. • Acknowledgements. The authors wish to thank the referee for valuable suggestions which helped to improve the paper. One of the authors (A.B. Thaheem) gratefully acknowledges the support provided by King Fahd University of Petroleum and Minerals during this research.",

year = "1997",

month = jan,

doi = "10.1515/dema-1997-0209",

language = "English",

volume = "30",

pages = "307--311",

journal = "Demonstratio Mathematica",

issn = "0420-1213",

publisher = "Walter de Gruyter GmbH",

number = "2",

}

TY - JOUR

T1 - On automorphisms of prime rings with involution

AU - Khan, L. A.

AU - Thaheem, A. B.

N1 - Funding Information: Now assume that a(x) = axa-1 for all x € R, a 6 R. Then by assumption, a2xa~2 = a* xa* for all x £ R. This implies that a*a2x = xa*a2 or a'aax — xa'a a = 0 for all x € R. Since a*a € Z(R), therefore rewriting the preceding equation we get ama(ax — xa) = 0 for all x 6 R. Since a"a is not a zero divisor, therefore ax = xa for all x 6 R and hence a is a central element. This proves that a = 1. The converse is simple. This completes the proof. • Acknowledgements. The authors wish to thank the referee for valuable suggestions which helped to improve the paper. One of the authors (A.B. Thaheem) gratefully acknowledges the support provided by King Fahd University of Petroleum and Minerals during this research.

PY - 1997/1

Y1 - 1997/1

UR - https://www.scopus.com/pages/publications/85053241769

U2 - 10.1515/dema-1997-0209

DO - 10.1515/dema-1997-0209

M3 - Article

AN - SCOPUS:85053241769

SN - 0420-1213

VL - 30

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EP - 311

JO - Demonstratio Mathematica

JF - Demonstratio Mathematica

IS - 2

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