Genus of numerical semigroups generated by three elements

Nari, Hirokatsu; Numata, Takahiro; Watanabe, Kei-ichi

doi:10.48550/arxiv.1104.3600

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Introduction2

Proof Consider the Action Of Gl1

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Cited by 3 publications

(3 citation statements)

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“…In Section 4 we will explore 3-generated numerical semigroup rings over a field and their almost Gorenstein property. Corollary 4.2 has been reported by H. Nari [14] (see [15] also) at the 32-nd Symposium on Commutative Algebra in Japan (Hayama, 2010). Our research is independent of [14,15].…”

Section: Introductionsupporting

confidence: 53%

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Almost Gorenstein rings

2013

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The notion of almost Gorenstein ring given by Barucci and Fröberg [2] in the case where the local rings are analytically unramified is generalized, so that it works well also in the case where the rings are analytically ramified. As a sequel, the problem of when the endomorphism algebra m : m of m is a Gorenstein ring is solved in full generality, where m denotes the maximal ideal in a given Cohen-Macaulay local ring of dimension one. Characterizations of almost Gorenstein rings are given in connection with the principle of idealization. Examples are explored.

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Section: Introductionsupporting

confidence: 53%

“…Corollary 4.2 has been reported by H. Nari [14] (see [15] also) at the 32-nd Symposium on Commutative Algebra in Japan (Hayama, 2010). Our research is independent of [14,15].…”

Section: Introductionsupporting

confidence: 53%

Almost Gorenstein rings

2013

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“…By results of Watanabe et al [24], δ(X l ) = l. Hence the Milnor number is 2δ = 2l, so e(JM (X l ), N D (X l )) = µ−2, and so e(JM (X l ), N D (X l )) plus the multiplicity over Y of the polar curve of…”

Section: Proof Consider the Action Of Glmentioning

confidence: 80%