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Abstract

Let \(R\) be a commutative Noetherian ring, \(I\) an ideal of \(R\), and \(M\) an \(R\)-module. The ambiguous structure of \(I\)-transform functor \(D_{I}(-)\) makes the study of its properties attractive. In this paper we gather conditions under which \(D_{I}(R)\) and \(D_{I}(M)\) appear in certain roles. It is shown under these conditions that \(D_{I}(R)\) is a Cohen–Macaulay ring, regular ring, \(\cdots\) and \(D_{I}(M)\) can be regarded as a Noetherian, flat, \(\cdots R\)-module. We also present a primary decomposition of zero submodule of \(D_{I}(M)\) and secondary representation of \(D_{I}(M)\).

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Correspondence to Y. Sadegh, J. A’zami or S. Yazdani.

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The authors declare that they have no conflicts of interest.

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MSC2010 numbers: 13D45; 14B15; 13E05

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Sadegh, Y., A’zami, J. & Yazdani, S. On the Ideal Transforms Defined by an Ideal. J. Contemp. Mathemat. Anal. 57, 399–404 (2022). https://doi.org/10.3103/S1068362322060073

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  • DOI: https://doi.org/10.3103/S1068362322060073

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