English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Suppose $m$ be a $12$-th power free integer. Let $K=\mathbb{Q}(\theta)$ be analgebraic number field defined by a complex root $\theta$ of an irreduciblepolynomial $x^{12}-m$ and $O_K$ be its ring of integers. In this paper, wedetermine the highest power of $p$ dividing the index of the subgroup$\Z[\theta]$ in $O_K$ and $p$-integral basis of $K$ for each prime $p$. These$p$-integral bases lead to the construction of an integral basis of $K$ whichis illustrated with examples. In particular, when $m$ is a square free integer,we provide necessary and sufficient conditions for the set$\{1,\theta,\theta^2,\cdots,\theta^{10},\theta^{11}\}$ to be an integral basisof $K.$

DISCRIMINANT and integral basis OF $\mathbb{Q}(\sqrt[12]{a})$