Rocky Mountain Journal of Mathematics

$\mathcal {W}$-Gorenstein $N$-complexes

Bo Lu, Jiaqun Wei, and Zhenxing Di

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Abstract

Given an integer $N\geq 2$ and a self-orthogonal subcategory $\mathcal {W}$ of an abelian category $\mathscr {A}$, we investigate the $\mathcal {W}$-Gorenstein $N$-complexes. We show that an $N$-complex $G$ is $\mathcal {W}$-Gorenstein if and only if $G$ is an $N$-complex consisting of $\mathcal {W}$-Gorenstein objects in $\mathscr {A}$. As an application, we improve a result of Estrada.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 6 (2019), 1973-1992.

Dates
First available in Project Euclid: 3 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1572746429

Digital Object Identifier
doi:10.1216/RMJ-2019-49-6-1973

Mathematical Reviews number (MathSciNet)
MR4027244

Subjects
Primary: 18G25: Relative homological algebra, projective classes
Secondary: 18G35: Chain complexes [See also 18E30, 55U15] 18E10: Exact categories, abelian categories

Keywords
$\mathcal {W}$ $N$-complex $\mathcal {W}$-Gorenstein $N$-complex $\mathcal {W}$-Gorenstein object Gorenstein injective $N$-complex.

Citation

Lu, Bo; Wei, Jiaqun; Di, Zhenxing. $\mathcal {W}$-Gorenstein $N$-complexes. Rocky Mountain J. Math. 49 (2019), no. 6, 1973--1992. doi:10.1216/RMJ-2019-49-6-1973. https://projecteuclid.org/euclid.rmjm/1572746429


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