On Stanley-Reisner rings of reduction number one
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 3, p. 605-610 
@article{ASNSP_2000_4_29_3_605_0,
     author = {Barile, Margherita and Morales, Marcel},
     title = {On Stanley-Reisner rings of reduction number one},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {3},
     year = {2000},
     pages = {605-610},
     zbl = {1012.13007},
     mrnumber = {1817711},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_3_605_0}
}

Barile, Margherita; Morales, Marcel. On Stanley-Reisner rings of reduction number one. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 3, pp. 605-610. http://www.numdam.org/item/ASNSP_2000_4_29_3_605_0/

[1] M. Barile - M. Morales, On the equations defining varieties of minimal degree, Comm. Algebra 28 (2000), 1223-1239. | MR 1742652 | Zbl 0971.14002

[2] D. Eisenbud - S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), 89-133. | MR 741934 | Zbl 0531.13015

[3] R. Fröberg, On Stanley-Reisner rings, Topics in Algebra 26, Part 2 (1990), 57-70. | MR 1171260 | Zbl 0741.13006

[4] J. Stückrad - W. Vogel, "Buchsbaum Rings and Applications", Springer, Berlin, 1986. | MR 881220 | Zbl 0606.13018