On certain invariants of idealizations

Nguyen Hong Loan

doi:10.1556/sscmath.51.2014.3.1288

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 51: Issue 3

On certain invariants of idealizations

Author:

Nguyen Hong Loan

Nguyen Hong Loan Vinh University Nghe An Vietnam

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Pages:: 357–365

Online Publication Date:: 26 Aug 2014

Publication Date:: 01 Sep 2014

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.51.2014.3.1288

Keywords:: Primary 13E05, 13H10; Idealization; polynomial type; polynomial type of fractions; Cohen-Macaulay module; pseudo Cohen-Macaulay module

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Let (R, m) be a Noetherian local ring and M a finitely generated R-module. In this paper, we study some invariants of the idealization R ⋉ M of R and M such as the polynomial type introduced by Cuong [2] and the polynomial type of fractions introduced by Cuong-Minh [3]. As consequences, we characterize the Cohen-Macaulay, generalized Cohen-Macaulay, pseudo Cohen-Macaulay and pseudo generalized Cohen-Macaulay properties of the idealization R ⋉ M.

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Studia Scientiarum Mathematicarum Hungarica

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