What is the history of clean rings?

Question

We recall that a ring is called a clean ring if each element is the sum of an idempotent and a unit.

Is there someone who can explain to me the history of the emergence of the definition of a clean ring? Why does the word "clean" appear in the definition of a clean ring?

Answer 1

In

Nicholson, W. Keith, and Yiqiang Zhou. "Clean rings: a survey." Advances in ring theory. 2005. 181-198.

It is stated that

This notion was introduced by Nicholson in [24] in 1977 in a study of exchange rings.

Where reference 24 is

Nicholson, W. Keith. "Lifting idempotents and exchange rings." Transactions of the American Mathematical Society 229 (1977): 269-278.

The name is, as far as I can tell, just an adjective selected at the time to use for reference. The term "exchange ring" though, is definitely suggestive of its defining property.

I'd also refer to these two references for the overall development of clean rings.