Abstract:In this paper, we introduce and study (weak) pure-injective Gorenstein projective modules. Let [Formula: see text] be an Artin algebra. We prove that the category of weak pure-injective Gorenstein projective left [Formula: see text]-modules coincides with the intersection of the category of pure-injective left [Formula: see text]-modules and that of Gorenstein projective left [Formula: see text]-modules. Then, we get an equivalent characterization of virtually Gorenstein algebras (being CM-finite). Furthermore… Show more
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