Clean Rings and Their Variations

T. Y. Lam ()
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T. Y. Lam: University of California, Berkeley, Department of Mathematics

Chapter 5 in Excursions in Ring Theory, 2026, pp 379-573 from Springer

Abstract: Abstract In Nicholson's seminal paper on suitable (or exchange) rings [Ni1] (c. 1977), he also introduced the notion of a clean ring. An element a in a ring R is said to be clean if a is the sum of an idempotent and a unit in R, and R is said to be a clean ring if every element in R is clean. Nicholson showed that, in any ring, clean elements are suitable, so in particular clean rings are always suitable (or exchange) rings.

Date: 2026
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DOI: 10.1007/978-3-032-26301-8_5

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