The number of elements in a minimal system of generators of the homogeneous ideal in the idealization ring

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The number of elements in a minimal system of generators of the homogeneous ideal in the idealization ring

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Let (R, m) be a noetherian local ring and M a finitely generated Rmodule. In this paper, we study the number of elements in a minimal system of generators of the homogeneous ideal in the idealization ring RnM. As immediate consequences, we presented a characterization for RnM being a regular local ring and homogeneous ideals of RnM being parameters ideals.

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