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the Boolean algebra of regular open sets in the Stone space of prime ideals of A. Each element x of A corresponds to the open set of prime ideals not containing x (which is open and closed, and therefore regular).
*The completion is the Boolean algebra of regular cuts of A. Here a cut is a subset U of A⁺ (the non-zero elements of A) such that if q is in U and p <= q then p is in U, and is called regular if whenever p is not in U there is some r <= p such that U has no elements <= r. Each element p of A corresponds to the cut of elements <= p.

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