Abstract
For a commutative ring R with identity, a Specker R-algebra is a commutative unital R-algebra generated by a Boolean algebra of idempotents, each nonzero element of which is faithful. Such algebras have arisen in the study of \(\ell \)-groups, idempotent-generated rings, Boolean powers of commutative rings, Pierce duality, and rings of continuous real-valued functions. We trace the origin of this notion from early studies of subgroups of bounded integer-valued functions to a variety of current contexts involving ring-theoretic, topological, and homological aspects of idempotent-generated algebras.
Dedicated to the memory of Elbert Walker
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Notes
- 1.
For background on \(\ell \)-groups, see [11, Ch. XIII].
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Bezhanishvili, G., Morandi, P.J., Olberding, B. (2020). Specker Algebras: A Survey. In: Nguyen, H., Kreinovich, V. (eds) Algebraic Techniques and Their Use in Describing and Processing Uncertainty. Studies in Computational Intelligence, vol 878. Springer, Cham. https://doi.org/10.1007/978-3-030-38565-1_1
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