Tokyo Journal of Mathematics

A Criterion for Dualizing Modules


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We establish a characterization of dualizing modules among semidualizing modules. Let $R$ be a finite dimensional commutative Noetherian ring with identity and $C$ a semidualizing $R$-module. We show that $C$ is a dualizing $R$-module if and only if $\mathrm{Tor}_i^R(E,E')$ is $C$-injective for all $C$-injective $R$-modules $E$ and $E'$ and all $i\geq 0$.

Article information

Tokyo J. Math., Volume 38, Number 1 (2015), 135-143.

First available in Project Euclid: 21 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13C05: Structure, classification theorems
Secondary: 13D07: Homological functors on modules (Tor, Ext, etc.) 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]


DIVAANI-AAZAR, Kamran; NIKKHAH BABAEI, Massoumeh; TOUSI, Massoud. A Criterion for Dualizing Modules. Tokyo J. Math. 38 (2015), no. 1, 135--143. doi:10.3836/tjm/1437506240.

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