%0 Journal Article 
%A Ara, Pere
%A Goodearl, Kenneth R.
%A Nielsen, Pace P.
%A O'Meara, Kevin C.
%A Pardo Espino, Enrique
%A Perera, Francesc
%A Perera
%T Levels of cancellation for monoids and modules
%D 2024
%U http://hdl.handle.net/10498/33230
%X 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.
%K Commutative monoid
%K cancellation
%K stable rank
%K refinement monoid
%K separativity
%K archimedean component
%K von Neumann regular ring
%K exchange ring
%~ Universidad de Cádiz