Advanced Search

A number field $K$, with ring of integers ${𝒪}_K$, is said to be a Pólya field if the ${𝒪}_K$-algebra formed by the integer-valued polynomials on ${𝒪}_K$ admits a regular basis. In a first part, we focus on fields with degree less than six which are Pólya fields. It is known that a field $K$ is a Pólya field if certain characteristic ideals are principal. Analogously to the classical embedding problem, we consider the embedding of $K$ in a Pólya field. We give a positive answer to this embedding problem by showing that...

A number field $K$, with ring of integers ${𝒪}_K$, is said to be a Pólya field when the ${𝒪}_K$-algebra formed by the integer-valued polynomials on ${𝒪}_K$ admits a regular basis. It is known that such fields are characterized by the fact that some characteristic ideals are principal. Analogously to the classical embedding problem in a number field with class number one, when $K$ is not a Pólya field, we are interested in the embedding of $K$ in a Pólya field. We study here two notions which can be considered as measures...