Geodesic
Derivations Whose Iterates are Zero or Invertible On a Left Ideal
Canadian mathematical bulletin, Tome 37 (1994) no. 1, pp. 124-132

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Let n ∊ Z+ and R be a ring which possesses a unit element, a left ideal J, and a derivation d such that dn (J) ≠ 0 and dn (r) is 0 or invertible, for all r ∊ J. We prove that either R is primitive, in which case R is Di with 1 ≤ i ≤ n+ 1, where Di is the ring of i × i matrices over a division ring D, or else there exist positive integers i, l and p with p prime and 2 ≤ ipl ≤ n + 1, such that R is where D is a division ring with characteristic p, and furthermore there is a derivation f of Di and a1, a2,..,al ∊ ZDi., the center of Di , such that a ∊ Di then and for all 2 ≤ j≤ l
DOI : 10.4153/CMB-1994-018-7
Mots-clés : 16W25, 16N60 
Tilly, Ben. Derivations Whose Iterates are Zero or Invertible On a Left Ideal. Canadian mathematical bulletin, Tome 37 (1994) no. 1, pp. 124-132. doi: 10.4153/CMB-1994-018-7
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     title = {Derivations {Whose} {Iterates} are {Zero} or {Invertible} {On} a {Left} {Ideal}},
     journal = {Canadian mathematical bulletin},
     pages = {124--132},
     year = {1994},
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     doi = {10.4153/CMB-1994-018-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-018-7/}
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