ABSTRACT
Let R denote a commutative ring. Idempotents of R are elements e ∈ R such that e 2 = e; examples are the additive and multiplicative identitiy elements 0 and 1. The set B(R) of idempotents of R forms a Boolean algebra with operations: e 1 ∩ e 2 = e 1 e 2 ; e 1 ∩ e 2 = e 1 + e 2 − e 1 e 2 ; e ′ = 1 − e ; 0 = 0 ; u = 1. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003071815/784c622f-41de-4d6a-a0dd-1da6961f4d1b/content/eq1061.tif"/>
