Geodesic
On local invertibility of functions of an $h$-complex variable
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2022), pp. 103-107

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The theory of functions of an $h$-complex variable is an alternative to the usual theory of functions of a complex variable, obtained by replacing the rules of multiplication. This change leads to the appearance of zero divisors on the set of $h$-complex numbers. Such numbers form a commutative ring that is not a field. $h$-Holomorphic functions are solutions of systems of equations of hyperbolic type, in comparison with classical holomorphic functions, which are solutions of systems of equations of elliptic type. A consequence of this is a significant difference between the properties of $h$-holomorphic functions and the classical ones. Interest in studying the properties of functions of an $h$-complex variable is associated with the need to search for new methods for solving problems in mechanics and the plane theory of relativity. The paper presents a theorem on the local invertibility of $h$-holomorphic functions, formulates the principles of preserving the domain and maximum of the norm.
Keywords: $h$-holomorphy; local invertibility; domain preservation principle; norm maximum principle; ring of $h$-complex numbers; zero divisors. 
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     title = {On local invertibility of functions of an $h$-complex variable},
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V. A. Pavlovsky; I. L. Vasiliev. On local invertibility of functions of an $h$-complex variable. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2022), pp. 103-107. http://geodesic.mathdoc.fr/item/BGUMI_2022_1_a10/