Thursday 30 Oct 2014: Direct Sum Decompositions of Modules over Local Rings
Roger Wiegand - University of Nebraska at Lincoln
Harrison 103 16:30-17:30
We exploit the analogy between decomposition of modules and factorization of integers. Unlike unique prime factorization in the integers, it's possible to have nonunique decomposition into indecomposable modules. For example, one can find indecomposable modules A, B, and C such that the direct sum of A and B is isomorphic to 100 copies of C. We state a theorem that describes exactly how badly uniqueness of direct sum decomposition can fail, and we give many examples.