On the Inverse Syzygy Problem
Co-author(s): Eva Zerz and Marcus Hausdorf
Reference: Communications in Algebra, 38 (2010) 2037-2047

A classical problem in computational algebra is the determination of the syzygy module of a given module. The inverse problem of deciding whether a given module is the syzygy module of another one has received much less attention, although it is of considerable interest in mathematical physics and control theory. In this article we generalise earlier results on this problem to a much larger class of rings. Classically, a positive answer to the inverse problem is related to torsionfreeness and the proofs require the use of quotient rings. Here it is shown that, by using the concept of torsionlessness, one can proof the central theorem without using quotients and thus for arbitrary coherent rings. As a by-product, we obtain an algorithm for determining certain extension groups.

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