Relative integral basis for algebraic number fields

Abstract

At first conditions are given for existence of a relative integral basis for OK≅Okn−1⊕I with [K;k]=n. Then the constrtiction of the ideal I in OK≅Okn−1⊕I is given for proof of existence of a relative integral basis for OK4(m1,m2)/Ok(​m3). Finally existence and construction of the relative integral basis for OK6(n3,−3)/Ok3(n3),OK6(n3,−3)/Ok2(−3) for some values of n are given.

Keywords

• finitely generated modules
• ring of integers
• ideals
• relative discriminant
• class numbers.