It is shown that there exist infinitely many cubic fields L with a power basis such that the splitting field M of L contains a given quadratic field K.

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Keywords Cubic fields, Power bases
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Journal Rocky Mountain Journal of Mathematics
Spearman, B.K. (Blair K.), & Williams, K.S. (2001). Cubic fields with a power basis. Rocky Mountain Journal of Mathematics, 31(3), 1103–1109. doi:10.1216/rmjm/1020171683