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- W2022148550 abstract "(1) Assume that R has no nonzero nil two-sided ideals. Let K ⩾ l be a fixed positive integer. The following two results are shown: (a) If, to each pair of elements x, y of R, there correspond positive integers m = m(x, y), n=n(x, y) ⩾ 1 such that […[[xm, yn], yn] …, yn]=0, k-times then R is commutative, (b) If a ϵ R is such that, to each y of R, there corresponds a positive integer n = n(a, y) ⩾ 1 such that […[[a, yn], yn] …, yn]=0, k-times then a is in the center of R. (2) Assume that R has no nonzero nil one-sided ideals. Then the same results as in (a) and (b) above are shown under the weaker assumptions that the k in (a) depends on the pair of elements x, y ϵ R and that the k in (b) depends on both a and y." @default.
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- W2022148550 date "1989-10-01" @default.
- W2022148550 modified "2023-09-30" @default.
- W2022148550 title "On a conjecture by Herstein" @default.
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- W2022148550 doi "https://doi.org/10.1016/0021-8693(89)90322-0" @default.
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