Abstract
A Noetherian ring integral over a central subring Σ is called injectively homogeneous if it has finite right injective dimension and the homological upper grades are equal for any two maximal ideals M and T with M ∩ Σ = T ∩ Σ. We show that this is a natural non-commutative analogue of Gorenstein rings. Among the properties shown are the Macaulay condition on Σ-sequences, stability under semiprime localisation and symmetry of the definition. Injective resolutions are described, as are examples.
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