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Transformations between Menger system

Ricci G.

Demonstratio Mathematica

2008

Vol. 41, nr 4

743-762

To define transformations between based universal algebras we must introduce representations that depend on the bases, contrary to what was possible for general vector spaces and believed possible for universal algebras. In fact, a counterex-ample shows that by representation-free transformations alone one cannot even ascertain whether a universal algebra has any dimension or not. A transformation notion, which can do, concerns basis dependent Menger systems. It enjoys a basic geometric property of universal algebras, the preservation of reference flocks, and generalizes the transformation groups of Linear Algebra into groupoids.