Add to ORKGLet L be a quartic number field with a quadratic subfield K. In 1986 Kawamoto gave a necessary and sufficient condition for L to have a normal relative integral basis (NRIB) over K. In this paper the authors explicitly construct a NRIB for L/K when such exists using their previous work on relative integral bases. The special cases when L is bicyclic, cyclic and pure are examined in detail. 1
AbstractK is a cyclic quartic extension of Q iff K = Q((rd + p d12)12), where d > 1, p and r are rat...
AbstractWhen does a cyclic quartic field have an integral basis over its quadratic subfield? A simpl...
AbstractSuppose thatL⊃Kare abelian extensions of the rationalsQwith Galois groups (Z/qsZ)nand (Z/qrZ...
Explicit conditions are given for a cyclic quartic field to have a relative integral basis over its ...
AbstractLet K be any number field, and let E be a quadratic or a biquadratic extension of K. We give...
AbstractLet L be a quartic number field with quadratic subfield Q([formula]). Then L = Q([formula], ...
AbstractLet L be a quartic number field with quadratic subfield Q([formula]). Then L = Q([formula], ...
Let L be a quartic number field with quadratic subfield Q([formula]). Then L = Q([formula], [formula...
An explicit normal relative integral basis is given for the normal closure of a pure cubic field ove...
Abstract. Cyclic quartic fields possessing a unique normal integral basis are characterized and the ...
Let K be a pure cubic field. Let L be the normal closure of K. A relative integral basis (RIB) for L...
AbstractWe develop an algorithm for computing all generators of relative power integral bases in qua...
Let K be a pure cubic field. Let L be the normal closure of K. A relative integral basis (RIB) for L...
Let L be a quartic number field with quadratic subfield K = Q(x/-c), where Q denotes the rational nu...
AbstractThe algorithms presented here make use of subfield information to improve computations. For ...
AbstractK is a cyclic quartic extension of Q iff K = Q((rd + p d12)12), where d > 1, p and r are rat...
AbstractWhen does a cyclic quartic field have an integral basis over its quadratic subfield? A simpl...
AbstractSuppose thatL⊃Kare abelian extensions of the rationalsQwith Galois groups (Z/qsZ)nand (Z/qrZ...
Explicit conditions are given for a cyclic quartic field to have a relative integral basis over its ...
AbstractLet K be any number field, and let E be a quadratic or a biquadratic extension of K. We give...
AbstractLet L be a quartic number field with quadratic subfield Q([formula]). Then L = Q([formula], ...
AbstractLet L be a quartic number field with quadratic subfield Q([formula]). Then L = Q([formula], ...
Let L be a quartic number field with quadratic subfield Q([formula]). Then L = Q([formula], [formula...
An explicit normal relative integral basis is given for the normal closure of a pure cubic field ove...
Abstract. Cyclic quartic fields possessing a unique normal integral basis are characterized and the ...
Let K be a pure cubic field. Let L be the normal closure of K. A relative integral basis (RIB) for L...
AbstractWe develop an algorithm for computing all generators of relative power integral bases in qua...
Let K be a pure cubic field. Let L be the normal closure of K. A relative integral basis (RIB) for L...
Let L be a quartic number field with quadratic subfield K = Q(x/-c), where Q denotes the rational nu...
AbstractThe algorithms presented here make use of subfield information to improve computations. For ...
AbstractK is a cyclic quartic extension of Q iff K = Q((rd + p d12)12), where d > 1, p and r are rat...
AbstractWhen does a cyclic quartic field have an integral basis over its quadratic subfield? A simpl...
AbstractSuppose thatL⊃Kare abelian extensions of the rationalsQwith Galois groups (Z/qsZ)nand (Z/qrZ...