Division in Associative $D$-Algebra

TL;DR

This paper explores division, division with remainder, and prime elements within associative D-algebras, proposing a framework for defining quotients as tensor products and analyzing algebraic properties.

Contribution

It introduces a novel approach to defining quotients as tensor products in associative D-algebras and discusses prime elements and division concepts.

Findings

Defined quotient as A⊗A-number in associative D-algebra

Analyzed division and division with remainder in this context

Proposed a definition for prime A-number

Abstract

From the symmetry between definitions of left and right divisors in associative $D$-algebra $A$, the possibility to define quotient as $A\otimes A$-number follows. In the paper, I considered division and division with remainder. I considered also definition of prime $A$-number.