Abstract
In this paper, we obtain necessary and sufficient conditions for all complete projective resolutions over a Morita ring [Formula: see text]. As special cases, we get a class of complete projective resolutions over [Formula: see text], from the ones over [Formula: see text] and [Formula: see text]. We also obtain necessary and sufficient conditions for all Gorenstein-projective modules over a Morita ring [Formula: see text]. As special cases, we get a class of Gorenstein-projective modules over [Formula: see text], from the ones over [Formula: see text] and [Formula: see text]. Furthermore, we determine all complete projective resolutions as well as all Gorenstein-projective modules over the [Formula: see text] matrix algebra [Formula: see text] over [Formula: see text].
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