LEVELS OF CANCELLATION FOR MONOIDS AND MODULES
Abstract Levels of cancellativity in commutative monoids M , determined by stable-rank values in $\mathbb {Z}_{> 0} \cup \{\infty \}$ for elements of M , are investigated. The behavior of the stable ranks of multiples $ka$ , for $k \in \mathbb {Z}_{> 0}$ and $a \in M$ , is determined. In the case of a refinement monoid M , the possible stable-rank values in archimedean components of M are pinned down. Finally, stable rank in monoids built from isomorphism or other equivalence classes of modules over a ring is discussed.
Authors
- Francesc Perera (ORCID: https://orcid.org/0000-0002-4669-4736)
- Pere Ara (ORCID: https://orcid.org/0000-0003-3739-9599)
- Pace P. Nielsen
- K.C. O’Meara (ORCID: https://orcid.org/0000-0002-8090-3466)
- Enrique Pardo (ORCID: https://orcid.org/0000-0002-1909-2895)
- K. R. Goodearl
Institutions
- Brigham Young University (US)
- Universitat Autònoma de Barcelona (ES)
- University of California, Santa Barbara (US)
- University of Canterbury (NZ)
- Universidad de Cádiz (ES)
Publication Details
- Journal
- Journal of the Australian Mathematical Society
- Published
- 2025-11-14
- DOI
- https://doi.org/10.1017/s144678872510133x
- Primary Topic
- Rings, Modules, and Algebras
- Type
- article
- Field-Weighted Citation Impact
- 0.00