Levels of cancellation for monoids and modules

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.