Cartan–Eilenberg Gorenstein Complexes with Respect to Duality Pairs

Abstract

In this paper, we consider Cartan–Eilenberg Gorenstein complexes with respect to duality pairs. Using the properties of duality pairs, we investigate Cartan–Eilenberg Gorenstein complexes. Moreover, we establish a relationship between Cartan–Eilenberg Gorenstein $(\mathscr{X}, \, \mathscr{Y})$-complexes and their terms for a duality pair $(\mathscr{X}, \, \mathscr{Y})$ of modules. Based on some facts given in this paper, we construct a new duality pair. Also, the Cartan–Eilenberg Gorenstein dimension of complexes is discussed.

Keywords

Cartan–Eilenberg Gorenstein $(\mathscr{X}, \, \mathscr{Y})$-injective complex / Cartan–Eilenberg Gorenstein $(\mathscr{X}, \, \mathscr{Y})$-projective complex / Cartan–Eilenberg Gorenstein $(\mathscr{X}, \, \mathscr{Y})$-flat complex / duality pair / 18G25 / 18G35 / 18E10

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