Local system equivalence

The important concept of the strict system equivalence of polynomial realisations has been extended to realisations over an arbitrary principal ideal domainR. We use the algebraic concept of the localisation of a ring at a prime ideal to study the local properties, as opposed to the global properties, of realisations over arbitrary principal ideal domains. This allows us to gain a new understanding of strict system equivalence. We show that twoR-realisations of aK-matrix, whereK is the field of fractions of the principal ideal domainR, are strictly system equivalent if and only if they are locally system equivalent at every prime ideal (p) ofR.