Monoids of modules and arithmetic of direct-sum decompositions
Monoids of modules and arithmetic of direct-sum decompositions
Let R be a (possibly noncommutative) ring and let C be a class of finitely generated (right) R-modules which is closed under finite direct sums, direct summands, and isomorphisms.Then the set V.C/ of isomorphism classes of modules is a commutative semigroup with operation induced by the direct sum.This semigroup encodes …