Factorization Theory and Decompositions of Modules
نویسندگان
چکیده
Let R be a commutative ring with identity. It often happens that M1 ⊕ · · · ⊕ Ms ∼= N1 ⊕ · · · ⊕ Nt for indecomposable R-modules M1, . . . , Ms and N1, . . . , Nt with s 6= t. This behavior can be captured by studying the commutative monoid {[M ] |M is an R-module} of isomorphism classes of R-modules with operation given by [M ]+[N ] = [M⊕N ]. 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.
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عنوان ژورنال:
- The American Mathematical Monthly
دوره 120 شماره
صفحات -
تاریخ انتشار 2013