Levels of cancellation for monoids and modules

Abstract

Levels of cancellativity in commutative monoids M, determined by stable-rank values in Z(>0)boolean OR { infinity } for elements of M, are investigated. The behavior of the stable ranks of multiples ka , for k is an element of Z(>0 )and alpha is an element of 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.