Address: Charles University, Faculty of Mathematics and Physics, Department of Algebra, Sokolovská 83, 186 75 Praha 8, Czech Republic
E-mail: ruzicka@karlin.mff.cuni.cz
Abstract: We develop elementary methods of computing the monoid $\boldsymbol\mathcal{V}(\boldsymbol\boldsymbolR)$ for a directly-finite regular ring $\boldsymbolR$. We construct a class of directly finite non-cancellative refinement monoids and realize them by regular algebras over an arbitrary field.
AMSclassification: primary 06F20; secondary 16E50, 16E20, 15A04.
Keywords: monoid, refinement, interpolation, ring, von Neumann regular.
DOI: 10.5817/AM2018-1-33