Journal of Commutative Algebra

On canonical modules of idealizations

Nguyen Thi Hong Loan

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Let $(R,\mathfrak {m})$ be a Noetherian local ring which is a quotient of a Gorenstein local ring. Let $M$ be a finitely generated $R$-module. In this paper, we study the structure of the canonical module $K(R\ \mathbb {n}\ M)$ of the idealization $R\ \mathbb {n}\ M$ via the polynomial type introduced by Cuong~\cite {C}. In particular, we give a characterization for $K(R\ \mathbb {n}\ M)$ being Cohen-Macaulay and generalized Cohen-Macaulay.

Article information

J. Commut. Algebra, Volume 9, Number 1 (2017), 107-117.

First available in Project Euclid: 5 April 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13C14: Cohen-Macaulay modules [See also 13H10] 13E05: Noetherian rings and modules

Idealization Cohen-Macaulay canonical module generalized Cohen-Macaulay canonical module


Loan, Nguyen Thi Hong. On canonical modules of idealizations. J. Commut. Algebra 9 (2017), no. 1, 107--117. doi:10.1216/JCA-2017-9-1-107.

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