Almost Gorenstein rings

Gotō, Shirō; Matsuoka, Naoyuki; Phuong, Tran Thi

doi:10.48550/arxiv.1106.1301

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2012

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Cited by 2 publications

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“…[1] and [12]). In [10], Goto, Matsuoka and Phuong studied, in particular, when Nagata's idealization produces an almost Gorenstein ring; the second author of the present paper studied the same problem for the duplication in his master thesis (see [19]). In this paper we characterize those ideals E of S for which S ⋊ ⋉ b E is almost symmetric, obtaining a numerical analogue of the results of [10].…”

Section: Introductionmentioning

confidence: 99%

The numerical duplication of a numerical semigroup

D'Anna¹,

Strazzanti²

2012

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In this paper we present and study the numerical duplication of a numerical semigroup, a construction that, starting with a numerical semigroup S and a semigroup ideal E ⊆ S, produces a new numerical semigroup, denoted by S ⋊ ⋉ b E (where b is any odd integer belonging to S), such that S = (S ⋊ ⋉ b E)/2. In particular, we characterize the ideals E such that S ⋊ ⋉ b E is almost symmetric and we determine its type. MSC: 20M14; 13H10.

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