Abstract
Let p be an odd prime, let \(K=\mathbb {Q}(\epsilon )\) where 𝜖 is a primitive cubic root of unity, and let L be the Kummer field \(\mathbb {Q}\left (\epsilon , \sqrt [3]{\alpha }\right )\). In this paper we obtain a characterization of the splitting behavior of the symbol algebras \(\left ( \frac {\alpha ,p}{K,\epsilon }\right )\) and \(\left ( \frac {\alpha ,p^{h_{p}}}{K,\epsilon }\right )\), where h p is the order in the class group \(Cl\left (L\right )\) of a prime ideal of \(\mathcal {O}_L\) which divides \(p\mathcal {O}_L.\)
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Acknowledgements
Since part of this work has been done when the first author visited the University “G. D’Annunzio” of Chieti-Pescara, she wants to thank the Department of Economic Studies of the University for the hospitality and the support. In addition, she wants to thank Professor Claus Fieker for the fruitful discussions about the computer algebra system MAGMA. The authors thank anonymous referees for their comments and suggestions which helped us to improve this paper.
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Savin, D., Acciaro, V. (2021). Some Split Symbol Algebras of Prime Degree. In: Cojocaru, A.C., Ionica, S., García, E.L. (eds) Women in Numbers Europe III. Association for Women in Mathematics Series, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-030-77700-5_11
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