<abstract xmlns="http://www.w3.org/1999/xhtml"> Let M = Q(i √d) be any imaginary quadratic field with a positive square-free d. Consider the polynomialf(x) = x3 − ax2 − (a + 3)x − 1with a parameter a ∈ ℤ. Let K = M(α), where α is a root of f. This is an infinite parametric family of sextic fields depending on two parameters, a and d. Applying relative Thue’s equations we determine the relative power integral bases of these sextic fields over their quadratic subfields. Using these results we also determine generators of (absolute) power integral bases of the sextic fields. </abstract>

Let M = Q(i √d) be any imaginary quadratic field with a positive square-free d. Consider the polynomialf(x) = x3 − ax2 − (a + 3)x − 1with a parameter a ∈ ℤ. Let K = M(α), where α is a root of f. This is an infinite parametric family of sextic fields depending on two parameters, a and d. Applying relative Thue’s equations we determine the relative power integral bases of these sextic fields over their quadratic subfields. Using these results we also determine generators of (absolute) power integral bases of the sextic fields.

Power integral bases in a family of sextic fields with quadratic subfields

University of Debrecen Mathematical Institute H–4010 Debrecen Pf.12. HUNGARY

University of Debrecen Mathematical Institute H-4010 Debrecen Pf.12. HUNGARY

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Power integral bases in a family of sextic fields with quadratic subfields"}

Let M = Q(i √d) be any imaginary quadratic field with a positive square-free d. Consider the polynomialf(x) = x3 − ax2 − (a + 3)x − 1with a parameter a ∈ ℤ....

Power integral bases in a family of sextic fields with quadratic subfields

Published Online: Feb 19, 2016

Page range: 59 - 66

Received: Oct 13, 2015

DOI: https://doi.org/10.1515/tmmp-2015-0041

Keywords
sextic fields, relative cubic extension, power integral basis, relative power integral basis

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Power integral bases in a family of sextic fields with quadratic subfields

Published Online: Feb 19, 2016

Page range: 59 - 66

Received: Oct 13, 2015

DOI: https://doi.org/10.1515/tmmp-2015-0041

Keywordssextic fields, relative cubic extension, power integral basis, relative power integral basis

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
sextic fields, relative cubic extension, power integral basis, relative power integral basis