Geodesic
On the Commutativity of a Ring with Identity
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 456-460

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Let R be a ring with identity. R satisfies one of the following properties for all x, y ∈ R: (I) xynxmy = xm+1yn+1 and mnm! n! x≠0 except x = 0; (II) xynxm = xm + 1yn + 1 and mm! n! x≠0 except x = 0; (III) xmyn = ynxm and m! n! x≠0 except x = 0; (IV) (xpyQ)n = xpnyqn for n = k, k + 1 and N(p, q, k) x≠0 except x = 0, where N(p, q, k) is a definite positive integer. Then R is commutative.
DOI : 10.4153/CMB-1984-071-x
Mots-clés : 16A70 
Tong, Jingcheng. On the Commutativity of a Ring with Identity. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 456-460. doi: 10.4153/CMB-1984-071-x
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     title = {On the {Commutativity} of a {Ring} with {Identity}},
     journal = {Canadian mathematical bulletin},
     pages = {456--460},
     year = {1984},
     volume = {27},
     number = {4},
     doi = {10.4153/CMB-1984-071-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-071-x/}
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