Linear equations over finite abelian groups
نویسنده
چکیده
One of the oldest problems in algebra is the solution of a system of linear equations over certain domains. The Gaussian elimination algorithm provides an effective solution over fields. The Smith normal form algorithm yields a method over the integers. Here we consider another variation of this theme. Let A be a finite (additive) abelian group, let αi,j ∈ End(A) for 1 ≤ i ≤ n and 1 ≤ j ≤ m and let b1, . . . , bm ∈ A. Then we want to determine the set S of all (x1, . . . , xn) ∈ A n with
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