Study-type determinants and their properties

TL;DR

This paper introduces the concept of Study-type determinants, explores their properties using a commutative diagram, and extends classical results like Dedekind's theorem with new inequalities and properties.

Contribution

It defines Study-type determinants and derives their properties, extending existing theorems and providing new insights into their mathematical structure.

Findings

Properties of Study-type determinants are established.

An inequality for degrees of representations is derived.

An extension of Dedekind's theorem is presented.

Abstract

In this paper, we define the concept of the Study-type determinant, and we present some properties of these determinants. These properties lead to some properties of the Study determinant. The properties of the Study-type determinants are obtained using a commutative diagram. This diagram leads not only to these properties, but also to an inequality for the degrees of representations and to an extension of Dedekind's theorem.