Tohoku Mathematical Journal
2021
September
SECOND SERIES VOL. 73, NO. 3

Tohoku Math. J.
73 (2021), 433-447

Title DEDEKIND'S CRITERION FOR THE MONOGENICITY OF A NUMBER FIELD VERSUS UCHIDA'S AND LÜNEBURG'S

Author Xavier Vidaux and Carlos R. Videla

(Received September 11, 2018, revised June 2, 2020)
Abstract. We compare three different characterizations, due respectively to R. Dedekind, K. Uchida, and H. Lüneburg, of when, given an algebraic integer, the ring generated by it coincides with the ring of integers of its quotient field, and apply our results to some concrete 2-towers of number fields.

Mathematics Subject Classification. Primary 11R04; Secondary 11U05.
Key words and phrases. Monogenic fields, Power basis, Integrally closed, Julia Robinson number, Totally real, Iterates of quadratic polynomials.

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