4 papers · 1 filter
Root Clusters and Multiclusters over Imperfect Hilbertian Fields
Shubham Jaiswal
We extend the theory of root clusters from perfect fields to general fields which are not necessarily perfect. We introduce the following notions for field extensions over any give…
On Variants of Inverse Cluster Size Problem & General Magnification
Shubham Jaiswal, M Krithika, P Vanchinathan
In this article we establish certain variants of the Inverse Cluster Size problem. We introduce the notion of primitive extensions and establish the Primitive variant of the proble…
Root Clusters over Number fields : Inverse Problems and Applications
Shubham Jaiswal
We develop the theory of root clusters further in this article and give some applications. We introduce some new notions as well as recall earlier notions for field extensions over…
On Minimal generating sets of splitting field, Cluster towers and Multiple transitivity of Galois groups
Shubham Jaiswal, P Vanchinathan
A natural generating set for a Galois extension regarded as the splitting field of an irreducible polynomial is introduced and investigated here. Minimal generating sets arising in…