IDEMPOTENT and NILPOTENT were used by Benjamin Peirce (1809-1880) in
1870 in American Journal of Mathematics (1881): "When an
expression...raised to a square or higher power...gives itself as the
result, it may be called idempotent" (OED2).
This raises at least three questions:
(0) Is that the correct spelling of Ben's last name?
(1) Which is the correct date: 1870 or 1881?
(2) As far as I can tell, the currently universally accepted
definition of idempotent is that which would be obtained from Pierce's
by striking the phrase "or higher power".
In using the conjunction "or", did Pierce mean to categorize as
an idempotent any element satisfying, say, (e)(e)(e) = e ? And if so,
when and how did the narrower usage come about?
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Prof. Randy K. Schwartz
Department of Mathematics
Liberal Arts Building
Schoolcraft College
18600 Haggerty Road
Livonia, MI 48152-2696 USA
email rschwart@schoolcraft.cc.mi.us
voice 734/462-4400 extn. 5290
fax 734/462-4558
"In the Inn of the world there is room for
_everyone_. To turn your back on even one
person, for whatever reason, is to run
the risk of losing the central piece of
your jigsaw puzzle." - Leo F. Buscaglia
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