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arXiv · 2001.08797

Specker Algebras: A Survey

Guram Bezhanishvili·Patrick J. Morandi·Bruce Olberding
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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.

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Guram Bezhanishvili, Patrick J. Morandi, Bruce Olberding. 2020-01-23. Specker Algebras: A Survey. https://arxiv.org/abs/2001.08797

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