Abstract
1. The idempotent Boolean ring, RO, and its ideals. The symbol R will be used throughout this paper to represent a ring and RO to represent the set of idempotent elements in the center of R. If a, bER0, we define the symbol (D by a ( b = (a - b) 2. The operation (D will be called idempotent addition. THEOREM 1.2 RO is a Boolean ring (called the idempotent Boolean ring of R) with respect to the operations of idempotent addition and multiplication. If e is a unit for R, then e is a unit for RO. PROOF. The proof is merely the verification of the fact that the postulates for a Boolean ring are satisfied. The reader may supply the details. LEMMA 1. If I is an ideal of R, and eCIO, then e is in the center of R.
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