Osaka Journal of Mathematics

The Socle of the Last Term in the Minimal Injective Resolution of a Gorenstein Module

Weiling Song, Xiaojin Zhang, and Zhaoyong Huang

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Abstract

Let $R$ be a left Noetherian ring, $S$ a right Noetherian ring and $_RU$ a Gorenstein module with $S={\rm End}(_RU)$. If the injective dimensions of $_RU$ and $U_S$ are finite, then the last term in the minimal injective resolution of $_{R}U$ has an essential socle.

Article information

Source
Osaka J. Math., Volume 56, Number 1 (2019), 123-132.

Dates
First available in Project Euclid: 16 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1547607630

Mathematical Reviews number (MathSciNet)
MR3908781

Zentralblatt MATH identifier
07055403

Subjects
Primary: 16E05: Syzygies, resolutions, complexes 16E10: Homological dimension 16E30: Homological functors on modules (Tor, Ext, etc.)

Citation

Song, Weiling; Zhang, Xiaojin; Huang, Zhaoyong. The Socle of the Last Term in the Minimal Injective Resolution of a Gorenstein Module. Osaka J. Math. 56 (2019), no. 1, 123--132. https://projecteuclid.org/euclid.ojm/1547607630


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