Derivations with Invertible Values
Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 300-310
Voir la notice de l'article provenant de la source Cambridge University Press
In this paper we study a question which, although somewhat special, has the virtue that its answer can be given in a very precise, definitive, and succinct way. It shows that the structure of a ring is very tightly determined by the imposition of a special behavior on one of its derivations.The problem which we shall examine is: Suppose that R is a ring with unit element, 1, and that d ≠ 0 is a derivation of R such that for every x ∊ R, d(x) = 0 or d(x) is invertible in R; must R then have a very special structure?As we shall see, the answer to this question is yes, in particular we show that except for a special case which occurs when 2R = 0, R must be a division ring D or the ring D 2 of 2 × 2 matrices over a division ring.
Bergen, Jeffrey; Herstein, I. N.; Lanski, Charles. Derivations with Invertible Values. Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 300-310. doi: 10.4153/CJM-1983-016-0
@article{10_4153_CJM_1983_016_0,
author = {Bergen, Jeffrey and Herstein, I. N. and Lanski, Charles},
title = {Derivations with {Invertible} {Values}},
journal = {Canadian journal of mathematics},
pages = {300--310},
year = {1983},
volume = {35},
number = {2},
doi = {10.4153/CJM-1983-016-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-016-0/}
}
TY - JOUR AU - Bergen, Jeffrey AU - Herstein, I. N. AU - Lanski, Charles TI - Derivations with Invertible Values JO - Canadian journal of mathematics PY - 1983 SP - 300 EP - 310 VL - 35 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-016-0/ DO - 10.4153/CJM-1983-016-0 ID - 10_4153_CJM_1983_016_0 ER -
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