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...
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Veröffentlicht in: | Journal of the Mathematical Society of Japan 2014, Vol.66 (2), p.641-646 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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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. |
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ISSN: | 0025-5645 1881-2333 |
DOI: | 10.2969/jmsj/06620641 |