Geodesic
Periodic and Nil Polynomials in Rings
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 473-476

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Let R be an associative ring and f(x1,..., xd) a polynomial in noncommuting variables. We say that f is periodic or nil in R if for all r1,..., rd ∈ R we have that f(r1,..., rd) is periodic, respectively nilpotent (recall that a ∈ R is periodic if for some integer ). 
Felzenszwalb, Bernardo; Giambruno, Antonino. Periodic and Nil Polynomials in Rings. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 473-476. doi: 10.4153/CMB-1980-072-5
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     author = {Felzenszwalb, Bernardo and Giambruno, Antonino},
     title = {Periodic and {Nil} {Polynomials} in {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {473--476},
     year = {1980},
     volume = {23},
     number = {4},
     doi = {10.4153/CMB-1980-072-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-072-5/}
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