A new family of polynomial identities for computing determinants

TL;DR

This paper introduces a new family of polynomial identities for computing determinants across various algebraic structures, including commutative, noncommutative, and nonassociative rings, and explores their properties.

Contribution

It presents novel definitions of determinants for diverse algebraic rings and investigates their fundamental properties, expanding the theoretical framework of determinant computation.

Findings

New determinant definitions for multiple algebraic structures

Properties of these determinants are systematically studied

Potential applications in algebra and computational mathematics

Abstract

We give new definitions for the determinant over commutative ring $K$, noncommutative ring $\mathbf{K}$, noncommutative ring $\mathcal{K}$ with associative powers, over noncommutative nonassociative ring $\mathfrak{K}$, and study their properties.