ON A THEOREM OF YEN
Main Article Content
Abstract
In [5] Yen showed that if $R$ is an associative ring with unity and $m > 1$ is a fixed integer such that $m =2(\text{ mod } 4)$ and $(x +y)^m =x^m +y^m$ for all $x$, $y$ in $R$, then $R$ must be commutative. In the present paper it is shown that commutativity is achieved even in the case where $m$ is dependent on $x$ and $y$.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
I. N. Herstein, "Power maps in rings," Mich. Math. J., 8 (1961), 29-32.
I. N. Herstein, Noncommutative Rings, Carus Math. Monograph No.15, Math. Assoc. Amer., Wiley, 1968.
N. Jacobson, "Structure theory for algebraic algebras of bounded degree," Ann. Math., 46 (1947), 695-707.
W. Streb, "Zur Struktur nichtcommutativer Ringe," Math. J. Okayama Univ., 31 (1989), 135-140.
C. T. Yen, "On a theorem of Herstein," Tamkang J. Math., 21 (1990), 123-130.
C. T. Yen, "A commutativity theorem for rings," Tamkang J. Math., 13 (1982), 243-246.