Gorenstein injective and projective complexes with respect to a semidualizing module
C Yang, L Liang - Communications in Algebra, 2012 - Taylor & Francis
C Yang, L Liang
Communications in Algebra, 2012•Taylor & FrancisLet R be a commutative (possibly non-Noetherian) ring (in order to make things less
technical) and C a semidualizing R-module. In this article, we introduce and investigate the
notion of GC-injective (GC-projective) complexes. This extends Enochs and García Rozas's
notion of Gorenstein injective (Gorenstein projective) complexes. We then show that a
complex X is GC-injective (GC-projective) if and only if X m is a GC-injective (GC-projective)
module for each m∈ ℤ.
technical) and C a semidualizing R-module. In this article, we introduce and investigate the
notion of GC-injective (GC-projective) complexes. This extends Enochs and García Rozas's
notion of Gorenstein injective (Gorenstein projective) complexes. We then show that a
complex X is GC-injective (GC-projective) if and only if X m is a GC-injective (GC-projective)
module for each m∈ ℤ.
Let R be a commutative (possibly non-Noetherian) ring (in order to make things less technical) and C a semidualizing R-module. In this article, we introduce and investigate the notion of G C -injective (G C -projective) complexes. This extends Enochs and García Rozas's notion of Gorenstein injective (Gorenstein projective) complexes. We then show that a complex X is G C -injective (G C -projective) if and only if X m is a G C -injective (G C -projective) module for each m ∈ ℤ.
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