Abelian Groups as Unions of Proper Subgroups
نویسنده
چکیده
Given a direct sum G of cyclic groups, we find a sharp bound for the minimal number of proper subgroups whose union is G. This problem generalizes to sums of cyclic modules over more general rings, such as local and Artinian rings or Dedekind domains and reduces to covering vector spaces by proper subspaces. As a consequence, we are also able to solve the analogous problem for monoids.
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