Radicals of systems of equations over strict total orders
A. Yu. Nikitin · Herald of Omsk University · 2019
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 studied. Some of the most important algebraic systems are partially ordered sets and graphs. This article attempts to construct algebraic geometry for strict partially ordered sets. The problem of determining the radical of system of equations is that solutions' set of the system can specify additional relationships on variables that aren't in the original system. The article explores such systems of equations and such finite strict total orders over which the radical of the system of equations can be built in a naive, in a certain sense, way (that is a system of equations with a simply constructed radical).