Let R be a commutative ring with identity. It often happens that M1 N1 Nt for indecomposable R-modules M1;:::; Ms and N1;:::; Nt with s6D t. This behavior can be captured by studying the commutative monoidfTMUj M is an R-moduleg of isomorphism classes of R-modules with operation given byTMUCTNUDTM NU. In this mostly self-contained exposition, we introduce the reader to the interplay between the the study of direct-sum decompositions of modules and the study of factorizations in integral domains.
['Nicholas R. Baeth', 'Roger Wiegand']
Factorization Theory and Decompositions of Modules