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SUMMARY:K.-i. Watanabe (Nihon University)
DTSTART:20210813T120000Z
DTEND:20210813T130000Z
DTSTAMP:20260423T020952Z
UID:VCAS/95
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/95/">In
 verse polynomials of symmetric numerical semigroups</a>\nby K.-i. Watanabe
  (Nihon University) as part of IIT Bombay Virtual Commutative Algebra Semi
 nar\n\n\nAbstract\nThis is a joint work with Kazufumi Eto (Nippon Institut
 e of Technology).\nThis work was inspired by the talk of M.E. Rossi (Univ.
  Genova) at VCAS on Dec. 1\, 2020.\nLet $H \\subset \\mathbb N$  be a nume
 rical semigroup ring and $k[H]$  be its semigroup ring over any field $K.$
  If $H = ⟨n_1\, \\ldots\,n_e)$\, we express $k[H]$ as $k[H] = k[x_1\,\\l
 dots\,x_e]/I_H$ and we want to express $k[H]/(t^h)$ by ”Inverse polynomi
 als” of Macaulay.\nWe study the defining ideal of a numerical semigroup 
 ring $k[H]$ using the inverse poly- nomial attached to the Artinian ring $
 k[H]/(t^h)$ for $h \\in H_+$. I believe this method to express by inverse 
 polynomials is very powerful and can be used for many purposes. At present
 \, we apply this method for the following cases.\n(1) To give a criterion 
 for H to be symmetric or almost symmetric.\n(2) Characterization of symmet
 ric numerical semigroups of small multiplicity.\n(3) A new proof of Bresin
 sky’s Theorem for symmetric semigroups generated by 4\nelements.\n
LOCATION:https://researchseminars.org/talk/VCAS/95/
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