A Boolean product R o B is defined for every ring R and every Boolean ring B, differing from the tensor product in that the left distributive law, r o (&1+&2) -r o fa +f2&, holds only if &i & 2 = 0 or 2r = 0. Every nonzero element of JR O B is uniquely expressible in the form X)*-i r < ° &*» where r,^r t^0 , fo^O, fabj -0 for j^i. Where they are meaningful, the commutative and associative laws and the distributive laws with respect to weak direct sums apply to the Boolean product operation, and

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... GF (2) is a unit with respect to the operation. The idempotent Boolean ring (R o B)° 493 AMERICAN MATHEMATICAL SOCIETY Uuly (see Bull. Amer. Math. Soc. Abstract 58-1-52) is isomorphic to R° o B. If R is biregular, so is R o B and relations are determined between the ideals of R, B, and Ro B.