On radicals and coordinate partial orders

Abstract

The solution of equations and systems of equations over real, complex, rational and integer numbers is a classic topic of research in various areas of mathematics for several thousand years. In the last 20 years, the so-called universal algebraic geometry has been actively developed, in which systems of equations over arbitrary algebraic systems are researched. Many practically important problems on finite graphs, finite fields, and finite orders can be formulated as problems related to solving systems of equations over these systems, which leads to the need to develop algebraic geometry. Many modern models of informational defence represents by graphs and partial orders (posets). This article presents polynomial algorithms for constructing radical and coordinate partial order of systems of equations over finite partial orders in a language without constants.