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monogenicfields.html
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<b><font size="+2">Monogenic Fields Data</font></b>
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<p><b>A monogenic number field is a number field whose ring of integers admits a power basis. <br>
Such a basis is often called a power integral basis. <br>
All quadratic fields and cyclotomic fields are monogenic.
Further, the maximal real subfield of a cyclotomic field is monogenic.<br>
An example, due to Dedekind, of a non-monogenic field is the field generated by a root of x^3-x^2-2x-8. <br>
The problem of characterizing all monogenic number fields is known as Hasse's problem.<br>
Below is a collection of some known families of monogenic fields.
Unless otherwise mentioned the power basis is generated by a root of the polynomial given below. <br>
Please send me an email if you have any corrections or families you'd like to see included. </b></p>
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<td ><i>Last modified on 8/16/2017.</i></td>
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