Waring's problem for commutative rings

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Abstract

For any prime number k ≥ 3 and any commutative ring A, we describe the subring Ak of A consisting of all sums of kth powers. For some k such as k = 11 or 19, we prove that every element of Ak is the sum of k3 kth powers (for any A). For the other k, we assume that the ring A is generated by 1 and t other elements to conclude that every element of Ak is the sum of k3t kth powers.

Original languageEnglish (US)
Pages (from-to)299-307
Number of pages9
JournalJournal of Number Theory
Volume26
Issue number3
DOIs
StatePublished - Jul 1987

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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