2008
DOI: 10.1016/j.jalgebra.2008.01.015
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Quasi-socle ideals in Gorenstein numerical semigroup rings

Abstract: Quasi-socle ideals, that is the ideals I of the form I = Q : m q in Gorenstein numerical semigroup rings over fields are explored, where Q is a parameter ideal, and m is the maximal ideal in the base local ring, and q 1 is an integer. The problems of when I is integral over Q and of when the associated graded ring G(I ) = n 0 I n /I n+1 of I is Cohen-Macaulay are studied. The problems are rather wild; examples are given.

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Cited by 9 publications
(5 citation statements)
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“…We put I = Q : m q and refer to those ideals as quasi-socle ideals in A. In this paper we are interested in the following question about quasi-socle ideals I, which are also the main subject of the researches [1][2][3]. The present research is a continuation of [1][2][3] and aims mainly at the analysis of the case where A is a complete intersection with dim A = 1.…”
Section: Introduction and The Main Resultsmentioning
confidence: 99%
See 4 more Smart Citations
“…We put I = Q : m q and refer to those ideals as quasi-socle ideals in A. In this paper we are interested in the following question about quasi-socle ideals I, which are also the main subject of the researches [1][2][3]. The present research is a continuation of [1][2][3] and aims mainly at the analysis of the case where A is a complete intersection with dim A = 1.…”
Section: Introduction and The Main Resultsmentioning
confidence: 99%
“…In this paper we are interested in the following question about quasi-socle ideals I, which are also the main subject of the researches [1][2][3]. The present research is a continuation of [1][2][3] and aims mainly at the analysis of the case where A is a complete intersection with dim A = 1. Following Heinzer and Swanson [4], for each parameter ideal Q in a Noetherian local ring (A, m) we define g(Q ) = max{q ∈ Z | Q : m q ⊆ Q } and call it the Goto number of Q .…”
Section: Introduction and The Main Resultsmentioning
confidence: 99%
See 3 more Smart Citations