A Look at Column-finite Matrices
نویسنده
چکیده
In this paper we consider the Z-module of integer-valued functions / defined on the nonnegative integers (respectively, on all integers) and characterize the submodule determined by the divisibility relation of the title and also, as a corollary, by the divisibility relation m+n\f(m)+f(n). Our results suggest some rather basic questions about such modules (equivalently, about infinite matrices of integers in which each column has only finitely many nonzero entries). We discuss these questions and pose a conjecture. The functions/from the nonnegative integers N to the integers Z satisfying
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