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Sums of cubes in polynomial rings. (English) Zbl 0711.11013
By studying sums of cubes in the ring F[x] of polynomials over a field F of characteristic $\ne 3$ and with cardinality $\ne 2$, 4, the author proves the nice result that for any associative ring A with a 1 and of prime characteristic $\ne 0,2,3$, every element in A is a sum of 3 cubes in A. The proof, which is by consideration of cases, took a great deal of computing time in searching for solutions and, in contrast with the result, is long and involved.
Reviewer: M.Dodson

MSC:
11C08Polynomials (number theory)
11P05Waring’s problem and variants
16U99Conditions on elements of noncommutative rings
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