On irreducible algebraic sets over linearly ordered semilattices
A.N. Shevlyakov
TL;DR
This paper investigates the structure of solution sets of equations over linearly ordered semilattices, identifying irreducible components and calculating their average number across all equations with a fixed number of variables.
Contribution
It provides a method to find irreducible components of equations over linearly ordered semilattices and computes the average number of such components for equations in n variables.
Findings
Identified irreducible components of solution sets for equations over linearly ordered semilattices.
Computed the average number of irreducible components for all equations with n variables.
Abstract
Equations over linearly ordered semilattices are studied. For any equation we find irreducible components of its solution set and compute the average number of irreducible components of all equations in variables.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory