Abstract
An element p of a ring is idempotent if p2 = p. A Boolean ring is a ring with unit in which every element is idempotent. Warning: a ring with unit is by definition a ring with a distinguished element 1 that acts as a multiplicative identity and that is distinct from the additive identity 0. The effect of the last proviso is to exclude from consideration the trivial ring consisting of 0 alone. The phrase “with unit” is sometimes omitted from the definition of a Boolean ring; in that case our present concept is called a “Boolean ring with unit.”
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© 1974 Springer-Verlag New York Inc.
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Halmos, P.R. (1974). Boolean Rings. In: Lectures on Boolean Algebras. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9855-7_1
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DOI: https://doi.org/10.1007/978-1-4612-9855-7_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90094-0
Online ISBN: 978-1-4612-9855-7
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