Abstract
Let be an irreducible polynomial of degree , and let be a root of . The purpose of this paper is to establish necessary and sufficient conditions for to be monogenic, meaning the ring of integers of is generated by the powers of a root of . Sufficient conditions for monogeneity are established using Dedekind’s criterion. We then apply the Montes algorithm to give an explicit formula for the discriminant of . Together, these results can be used to determine when is not monogenic.
Citation
T. Alden Gassert. "A NOTE ON THE MONOGENEITY OF POWER MAPS." Albanian J. Math. 11 (1) 3 - 12, 2017. https://doi.org/10.51286/albjm/1495919797
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