On finitely generated module whose first nonzero fitting ideal is maximal |
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Authors: | S Hadjirezaei S Hedayat |
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Institution: | 1. Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran;2. Department of Pure Mathematics, Shahid Bahonar University Kerman, Kerman, Islamic Republic of Iran |
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Abstract: | Let R be a Noetherian ring and M be a finitely generated R-module. Let I(M) be the first nonzero Fitting ideal of M. The main result of this paper asserts that when I(M) = Q is a regular maximal ideal of R, then M?R∕Q⊕P, for some projective R-module P of constant rank if and only if T(M)?QM. As a consequence, it is shown that if M is an Artinian R-module and I(M) = Q is a regular maximal ideal of R, then M?R∕Q. |
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Keywords: | Artinian module fitting ideal minimal free presentation torsion submodule |
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