Finite Equation Tests for Pure Sub-acts and Right Coherency of Monoids
DOI:
https://doi.org/10.31185/bsj.Vol23.Iss46.1751Keywords:
monoid; right act; sub-act; right coherent monoid; purity; finite presentation; kernel congruence; rewriting system.Abstract
This paper gives a finite-kernel procedure for extracting presentations of finitely generated sub-acts of finitely presented right acts. For a tuple , we use the canonical map and its kernel congruence . We prove that is finitely presented if and only if is finitely generated, and we derive a finite-kernel characterization of right coherent monoids. We also formulate finite equation tests for purity and a rewriting criterion for extracting defining relations. A numerical maintenance-state model computes the kernel, a finite presentation, and the risk totals before and after maintenance. The results turn abstract coherency statements into an explicit verification procedure.
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