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Satoru Kimura, Tran Thi Phuong,  Hoang Le Truong (2010). Quasi-socle ideals and Goto numbers of parameters. Journal of Pure and Applied Algebra, Volume 214, Issue 5, May 2010, pp. 501-511.

Abstract. Goto numbers for certain parameter ideals Q in a Noetherian local ring (A,m) with Gorenstein associated graded ring are explored. As an application, the structure of quasi-socle ideals (q≥1) in a one-dimensional local complete intersection and the question of when the graded rings are Cohen–Macaulay are studied in the case where the ideals I are integral over Q.