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Algebra |
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Authors: Egor Sibrin, Vladimir Orlov
This work presents the framework of Nonliquent Mathematics (NL), a commutative extension of the real numbers that defines division by zero through the introduction of an idempotent element denoted by ї=1/0 and the distinction between a true zero and a special zero. The algebraic operations of addition, multiplication, division, conjugation, and root extraction are formulated in this system, along with Taylor expansions for basic functions and a consistent differential and integral calculus adapted to NL variables. A Hilbert space of NL-valued functions is defined with a corresponding inner product, and a modified form of the Navier—Stokes equation is derived within this framework. Two particular solutions of the modified equation are obtained for the cases of zero and nonzero viscosity, demonstrating the consistency and potential applications of NL in analysis and fluid dynamics.
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