RINGS IN WHICH ELEMENTS ARE UNIQUELY THE SUM OF AN IDEMPOTENT AND A UNIT
Glasgow mathematical journal, Tome 46 (2004) no. 2, pp. 227-236
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An associative ring with unity is called clean if every element is the sum of an idempotent and a unit; if this representation is unique for every element, we call the ring uniquely clean. These rings represent a natural generalization of the Boolean rings in that a ring is uniquely clean if and only if it is Boolean modulo the Jacobson radical and idempotents lift uniquely modulo the radical. We also show that every image of a uniquely clean ring is uniquely clean, and construct several noncommutative examples.
NICHOLSON, W. K.; ZHOU, Y. RINGS IN WHICH ELEMENTS ARE UNIQUELY THE SUM OF AN IDEMPOTENT AND A UNIT. Glasgow mathematical journal, Tome 46 (2004) no. 2, pp. 227-236. doi: 10.1017/S0017089504001727
@article{10_1017_S0017089504001727,
author = {NICHOLSON, W. K. and ZHOU, Y.},
title = {RINGS {IN} {WHICH} {ELEMENTS} {ARE} {UNIQUELY} {THE} {SUM} {OF} {AN} {IDEMPOTENT} {AND} {A} {UNIT}},
journal = {Glasgow mathematical journal},
pages = {227--236},
year = {2004},
volume = {46},
number = {2},
doi = {10.1017/S0017089504001727},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089504001727/}
}
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