Apostolova, Lilia N. Hyperbolic fourth-\(\mathbb R\) quadratic equation and holomorphic fourth-\(\mathbb R\) polynomials. (English) Zbl 1291.30023 Math. Balk., New Ser. 26, No. 1-2, 15-24 (2012). Summary: the algebra \(\mathbb R(1,j,j^2,j^3)\), \(j^4=-1\) of the fourth-\(\mathbb R\) numbers, or in other words the algebras of the double-complex numbers \(\mathbb C(1,j)\) and the corresponding functions, were studied in the paper of S. Dimiev et al. The hyperbolic fourth-\(\mathbb R\) numbers form other similar to \(\mathbb C(1,j)\) algebra with zero divisors. In this note the square roots of hyperbolic fourth-\(\mathbb R\) numbers and hyperbolic complex numbers are found. The quadratic equation with hyperbolic fourth-\(\mathbb R\) coefficients and variables is solved. The Cauchy-Riemann system for holomorphicity of fourth-\(\mathbb R\) functions is recalled. Holomorphic homogeneous polynomials of fourth-\(\mathbb R\) variables are listed. MSC: 30C10 Polynomials and rational functions of one complex variable 32A30 Other generalizations of function theory of one complex variable 30G35 Functions of hypercomplex variables and generalized variables Keywords:algebra of fourth-\(\mathbb R\) numbers; algebra of hyperbolic fourth-\(\mathbb R\) numbers; hyperbolic fourth-\(\mathbb R\) quadratic equation; holomorphic fourth-\(\mathbb R\) function; holomorphic fourth-\(\mathbb R\) polynomial PDFBibTeX XMLCite \textit{L. N. Apostolova}, Math. Balk., New Ser. 26, No. 1--2, 15--24 (2012; Zbl 1291.30023)