Primitive element: Difference between revisions
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In [[field theory (mathematics)|field theory]], a branch of [[mathematics]], a '''primitive element''' of a [[finite field]] ''GF''(''q'') is a [[generating set of a group|generator]] of the [[group of units|multiplicative group]] of the field, which is necessarily [[cyclic group|cyclic]]. | In [[field theory (mathematics)|field theory]], a branch of [[mathematics]], a '''primitive element''' of a [[finite field]] ''GF''(''q'') is a [[generating set of a group|generator]] of the [[group of units|multiplicative group]] of the field, which is necessarily [[cyclic group|cyclic]]. | ||
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* {{cite book | last=Jacobson | first=Nathan | authorlink=Nathan Jacobson | title=Basic Algebra I | edition=2nd ed | year=1985 | publisher=W. H. Freeman and Co. | place=New York | isbn=978-0-7167-1480-4 }} | * {{cite book | last=Jacobson | first=Nathan | authorlink=Nathan Jacobson | title=Basic Algebra I | edition=2nd ed | year=1985 | publisher=W. H. Freeman and Co. | place=New York | isbn=978-0-7167-1480-4 }} | ||
* {{cite book | last=Lidl | first=Rudolf | coauthors=Harald Niederreiter | title=Finite Fields | edition=2nd ed | year=1997 | publisher=[[Cambridge University Press]] | isbn=0-521-39231-4 }} | * {{cite book | last=Lidl | first=Rudolf | coauthors=Harald Niederreiter | title=Finite Fields | edition=2nd ed | year=1997 | publisher=[[Cambridge University Press]] | isbn=0-521-39231-4 }} | ||
Revision as of 13:54, 27 October 2008
In field theory, a branch of mathematics, a primitive element of a finite field GF(q) is a generator of the multiplicative group of the field, which is necessarily cyclic.
See also
References
- Jacobson, Nathan (1985). Basic Algebra I, 2nd ed. W. H. Freeman and Co.. ISBN 978-0-7167-1480-4.
- Lidl, Rudolf; Harald Niederreiter (1997). Finite Fields, 2nd ed. Cambridge University Press. ISBN 0-521-39231-4.