Geodesic
Rings with a Special Kind of Automorphism
Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 3-8

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In this paper we examine the nature of rings R with unit having an automorphism φ ≠ 1 such that x — φ(x) is 0 or invertible for every x ∊ R. We show that the only examples of such rings are R = D, R = D2 , and R = D ⊕ D, where D is a division ring. Furthermore, for the case D2 , we describe the division rings that are possible.
DOI : 10.4153/CMB-1983-001-9
Mots-clés : 16A72 
Bergen, Jeffrey; Herstein, I. N. Rings with a Special Kind of Automorphism. Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 3-8. doi: 10.4153/CMB-1983-001-9
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     title = {Rings with a {Special} {Kind} of {Automorphism}},
     journal = {Canadian mathematical bulletin},
     pages = {3--8},
     year = {1983},
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     number = {1},
     doi = {10.4153/CMB-1983-001-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-001-9/}
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