Wang's theorem for one-dimensional local rings

In this article, we show that, Q:_A\frak{m}^t\subseteq\frak{m}^t for all integers t > 0, and for all parameter ideals Q\subseteq\frak{m}^{2t-1} in a one-dimensional Cohen-Macaulay local ring (A,\frak{m}) provided that A is not a regular local ring. The assertion obtained by Wang can be extended t...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of the Mathematical Society of Japan 2014, Vol.66 (2), p.641-646
Hauptverfasser: HORIUCHI, Jun, SAKURAI, Hideto
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In this article, we show that, Q:_A\frak{m}^t\subseteq\frak{m}^t for all integers t > 0, and for all parameter ideals Q\subseteq\frak{m}^{2t-1} in a one-dimensional Cohen-Macaulay local ring (A,\frak{m}) provided that A is not a regular local ring. The assertion obtained by Wang can be extended to one-dimensional (hence, arbitrary dimensional) local rings after some mild modifications. We refer to these quotient ideals I = Q:_A\frak{m}^t, t-th quasi-socle ideals of Q. Examples are explored.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/06620641