Abstract
We present and study the concept of m-periodic Gorenstein objects relative to a pair (A,B) of classes of objects in an abelian category, as a generalization of m-strongly Gorenstein projective modules over associative rings. We prove several properties when (A,B) satisfies certain homological conditions, like for instance when (A,B) is a GP-admissible pair. Connections to Gorenstein objects and Gorenstein homological dimensions relative to these pairs are also established.
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