Two-dimensional left (right) unital algebras over algebraically closed fields and $\mathbb{R}$

Abstract

In this paper we describe all, up to isomorphism, left unital, right unital and unital algebra structures on two-dimensional vector space over any algebraically closed field and $\mathbb{R}$. We tabulate the algebras with the units.

A type-mistake in $A_{3,2}(\mathbf{c})$ case, page 3, and its consequences are corrected