A pseudo-Gorenstein graded ring becomes Gorenstein when the trace ideal of its canonical module contains a length-two regular sequence in the initial degree, with applications to nearly and almost Gorenstein rings.
Aoyama,Some basic results on canonical modules, Journal of Mathematics of Kyoto University23(1983), no
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When do pseudo-Gorenstein rings become Gorenstein?
A pseudo-Gorenstein graded ring becomes Gorenstein when the trace ideal of its canonical module contains a length-two regular sequence in the initial degree, with applications to nearly and almost Gorenstein rings.