@unpublished{10498/33230,
year = {2024},
month = {9},
url = {http://hdl.handle.net/10498/33230},
abstract = {Levels of cancellativity in commutative monoids M, determined by stable rank values in Z>0 ∪ {∞} for elements of M, are investigated. The behavior of the stable ranks of multiples ka, for k ∈ Z>0 and a ∈ 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.},
organization = {The first and sixth authors were partially supported by the Spanish State Research Agency (grant No. PID2020-113047GB-I00/AEI/10.13039/501100011033), by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya (grant No. 2017-SGR-1725) and by the Spanish State Research Agency through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). The third author was partially supported by the Simons Foundation (grant #963435). The third and fourth authors thank the Mathematics Department of the Universitat Autònoma de Barcelona for hospitality during their visits, and the fourth author also thanks the Mathematics Departments of the University of California, Santa Barbara and the Universidad de Cádiz for their hospitality during the early part of this project. The fifth author was partially supported by PAI III grant FQM- 298 of the Junta de Andalucía, by the DGI-MINECO and European Regional Development Fund, jointly, through grant PID2020-113047GB-I00, and by the grant “Operator Theory: an interdisciplinary approach”, reference ProyExcel 00780, a project financed in the 2021 call for Grants for Excellence Projects, under a competitive bidding regime, aimed at entities qualified as Agents of the Andalusian Knowledge System, in the scope of the Plan Andaluz de Investigación, Desarrollo e Innovación (PAIDI 2020), Consejería de Universidad, Investigación e Innovación of the Junta de Andalucía.},
publisher = {arXiv},
keywords = {Commutative monoid},
keywords = {cancellation},
keywords = {stable rank},
keywords = {refinement monoid},
keywords = {separativity},
keywords = {archimedean component},
keywords = {von Neumann regular ring},
keywords = {exchange ring},
title = {Levels of cancellation for monoids and modules},
author = {Ara, Pere and Goodearl, Kenneth R. and Nielsen, Pace P. and O'Meara, Kevin C. and Pardo Espino, Enrique and Perera, Francesc and Perera},
}