Coordinatization of lattices by regular rings without unit and Banaschewski functions

  title={Coordinatization of lattices by regular rings without unit and Banaschewski functions},
  author={Friedrich Wehrung},
A Banaschewski function on a bounded lattice L is an antitone self-map of L that picks a complement for each element of L. We prove a set of results that include the following: • Every countable complemented modular lattice has a Banaschewski function with Boolean range, the latter being unique up to isomorphism. • Every (not necessarily unital) countable von Neumann regular ring R has a map ε from R to the idempotents of R such that xR = ε(x)R and ε(xy) = ε(x)ε(xy)ε(x) for all x, y ∈ R… CONTINUE READING

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