Geodesic
A Commutattvity Theorem for Rings and Groups
Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 419-423

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The following theorem is proved: Suppose R is a ring with identity which satisfies the identities xkyk = ykxk and xlyl = ylxl , where k and l are positive relatively prime integers. Then R is commutative. This theorem also holds for a group G. Furthermore, examples are given which show that neither R nor G need be commutative if either of the above identities is dropped. The proof of the commutativity of R uses the fact that G is commutative, where G is taken to be the group R* of units in R.
DOI : 10.4153/CMB-1979-055-9
Mots-clés : 16A70, 20F10, 16A38 
Nicholson, W. K.; Yaqub, Adil. A Commutattvity Theorem for Rings and Groups. Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 419-423. doi: 10.4153/CMB-1979-055-9
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     author = {Nicholson, W. K. and Yaqub, Adil},
     title = {A {Commutattvity} {Theorem} for {Rings} and {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {419--423},
     year = {1979},
     volume = {22},
     number = {4},
     doi = {10.4153/CMB-1979-055-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-055-9/}
}
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