Homology, Homotopy and Applications

Model structures on modules over Ding-Chen rings

James Gillespie

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An n-FC ring is a left and right coherent ring whose left and right self-FP-injective dimension is n. The work of Ding and Chen shows that these rings possess properties which generalize those of n-Gorenstein rings. In this paper we call a (left and right) coherent ring with finite (left and right) self-FP-injective dimension a Ding-Chen ring. In the case of Noetherian rings, these are exactly the Gorenstein rings. We look at classes of modules we call Ding projective, Ding injective and Ding flat which are meant as analogs to Enochs' Gorenstein projective, Gorenstein injective and Gorenstein flat modules. We develop basic properties of these modules. We then show that each of the standard model structures on Mod-R, when R is a Gorenstein ring, generalizes to the Ding-Chen case. We show that when R is a commutative Ding-Chen ring and G is a finite group, the group ring R[G] is a Ding-Chen ring.

Article information

Homology Homotopy Appl., Volume 12, Number 1 (2010), 61-73.

First available in Project Euclid: 28 January 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18G35: Chain complexes [See also 18E30, 55U15] 55U35: Abstract and axiomatic homotopy theory

Model structure Ding-Chen ring


Gillespie, James. Model structures on modules over Ding-Chen rings. Homology Homotopy Appl. 12 (2010), no. 1, 61--73. https://projecteuclid.org/euclid.hha/1296223822

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