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Paper   IPM / M / 16694
School of Mathematics
  Title:   Existence of relative integral basis over quadratic fields and Polya property
  Author(s):  Abbas Maarefparvar
  Status:   Published
  Journal: Acta Math. Hungar.
  Vol.:  164
  Year:  2021
  Pages:   593-598
  Supported by:  IPM
  Abstract:
For L/K a finite extension of algebraic number fields, L may or may not have a relative integral basis over K. In this paper, we show the existence of relative integral basis of a biquadratic field L=\mathbbQ(√m,√n) over its quadratic subfield K=\mathbbQ(√m) is equivalent to that K is a Pólya field, or equivalently all strongly ambiguous ideal classes of K are trivial.

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