The classification of two-dimensional nonassociative algebras (Q1977517)

In this important paper, the author provides a complete classification of two-dimensional nonassociative algebras over arbitrary base fields including those of characteristic two. The key to his classification is the notion of unital heart. This paper completes the two-dimensional part of the classification project begun in the seminal paper of \textit{Benjamin Peirce} [Linear associative algebras, Am. J. Math. 4, 99-215 (1881), addenda: 215-229 (pp. 225-229 by Charles S. Pierce)].