Tame and wild refinement monoids

P. Ara, K. R. Goodearl

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

© 2014, Springer Science+Business Media New York. The class of refinement monoids (commutative monoids satisfying the Riesz refinement property) is subdivided into those which are tame, defined as being an inductive limit of finitely generated refinement monoids, and those which are wild, i.e., not tame. It is shown that tame refinement monoids enjoy many positive properties, including separative cancellation (2x=2y=x+y⇒x=y) and multiplicative cancellation with respect to the algebraic ordering (mx≤my⇒x≤y). In contrast, examples are constructed to exhibit refinement monoids which enjoy all the mentioned good properties but are nonetheless wild.
Original languageEnglish
JournalSemigroup Forum
Volume91
Issue number1
DOIs
Publication statusPublished - 26 Aug 2015

Keywords

  • Exchange rings
  • Graph monoids
  • Non-stable K-theory
  • Refinement monoids
  • von Neumann dimension
  • von Neumann regular rings

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