The isomorphism problem for monoid rings of rank 2 monoids Original Research Article

The main result of this paper is that for a commutative ring R and finitely generated submonoids M and N of image2 the monoid rings R[M] and R[N] are isomorphic as R algebras if and only if M and N are isomorphic. In the course of proof we derive various results concerning the structure of rank 2 monoids and isomorphisms between the corresponding monoid rings.