5 papers
An Algebraic Approach to the Fundamental Theorem of Algebra
Priyabrata Mandal, Sajad A. Sheikh
In this paper, we investigate the algebraic counterpart of the Fundamental Theorem of Algebra. We explore the concept of real closed fields and quadratic forms. We show, by means o…
Totally positive field extensions and the pythagorean index
Priyabrata Mandal, Preeti Raman, Abhay Soman
For a formally real field , we study totally positive field extensions over . We show that, if is Galois and totally positive then so is the corresponding extensio…
Divisibility relation between the number of certain surjective group and ring homomorphisms
Sonu Kumar, Priyabrata Mandal
In this article, we identify the existence of a divisibility relationship between the number of ring homomorphisms and surjective group homomorphisms. We demonstrate that for finit…
Weak isotropy of central simple algebras with orthogonal involutions over totally positive field extensions
Priyabrata Mandal, Abhay Soman
In this paper, we explore the behavior of orthogonal involutions in the context of totally positive field extensions. Let be a totally positive extension of formally real fie…
On Certain Diophantine Equations Involving Lucas Numbers
Priyabrata Mandal
This paper explores the intricate relationships between Lucas numbers and Diophantine equations, offering significant contributions to the field of number theory. We first establis…