8 papers
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…
A Generalization of a Theorem of Nakajima-Landweber-Stong
Shubham Jaiswal, Tony J. Puthenpurakal
The main result of this paper is a generalization of a theorem of Nakajima-Landweber-Stong to the modular invariant rings of transvection groups over Dedekind domains. More precise…
The Regular property of Invariant Rings over Regular Domains
Shubham Jaiswal, Tony J. Puthenpurakal
The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudo-reflection groups over regular domains. More precis…
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…
Cluster Magnification, Root Capacity, Unique Chains and Base Change
Chandrasheel Bhagwat, Shubham Jaiswal
This article is inspired from the work of M Krithika and P Vanchinathan on Cluster Magnification and the work of Alexander Perlis on Cluster Size. We establish the existence of pol…
Right Splitting, Galois Correspondence, Galois Representations and Inverse Galois Problem
Chandrasheel Bhagwat, Shubham Jaiswal
In this article, we realize some groups as Galois groups over rational numbers and finite extension of rational numbers by studying right splitting of some exact sequences, Galois…