A formula for ideal lattices of general commutative rings

Details A formula for ideal lattices of general commutative rings A formula for ideal lattices of general commutative rings

2006-01-16

arxiv.org/abs/math/0601377v2

Mathematics

Commutative Algebra

9 pages

Scientific paper

Let S be a set of n ideals of a commutative ring A. Let G_{even} (respectively G_{odd}) denote the product of all the sums of even (respectively odd) number of ideals of S. If n<7 the product of G_{even} and the intersection of all ideals of S is included in G_{odd}. 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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