The cl-core of an ideal

• Autores: Louiza Fouli, Janet C. Vassilev
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 149, Nº 2, 2010, págs. 247-262
• Idioma: inglés
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• Resumen

  • We expand the notion of core to cl-core for Nakayama closures cl. In the characteristic p > 0 setting, when cl is the tight closure, denoted by *, we give some examples of ideals when the core and the *-core differ. We note that *-core(I) = core(I), if I is an ideal in a one-dimensional domain with infinite residue field or if I is an ideal generated by a system of parameters in any Noetherian ring. More generally, we show the same result in a Cohen�Macaulay normal local domain with infinite perfect residue field, if the analytic spread, l, is equal to the *-spread and I is Gl and weakly-(l - 1)-residually S2. This last is dependent on our result that generalizes the notion of general minimal reductions to general minimal *-reductions. We also determine that the *-core of a tightly closed ideal in certain one-dimensional semigroup rings is tightly closed and therefore integrally closed.