A Formula for Ideal Lattices of General Commutative Rings

نویسندگان

  • TAKASHI AOKI
  • SHUZO IZUMI
  • YASUO OHNO
  • MANABU OZAKI
چکیده

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.

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تاریخ انتشار 2006