Let be a polynomial ring over a field . Let be a simplicial complex whose vertex set is contained in . For an integer , we investigate the -Buchsbaum property of residue class rings and for the Stanley–Reisner ideal . We characterize the -Buchsbaumness of such rings in terms of the simplicial complex and the power . We also give a characterization in the case where is the edge ideal of a simple graph.
Nguyên Công Minh. Yukio Nakamura. "On the -Buchsbaum property of powers of Stanley–Reisner ideals." Nagoya Math. J. 213 127 - 140, March 2014. https://doi.org/10.1215/00277630-2394073