Abstract
Let R be a commutative ring, with an identity element. It is the purpose of this note to establish conditions for an arbitrary but fixed ideal a of R to satisfy the distributive lawfor all ideals b and c of R. In particular, in the Noetherian case, this will be related to the decomposition of a into prime ideals. We start withProposition 1. For a fixed ideal a in a commutative ring R with an identity element, the following conditions are equivalent.
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