Waring's problem for commutative rings

L. N. Vaserstein

doi:10.1016/0022-314X(87)90086-2

Waring's problem for commutative rings

L. N. Vaserstein

Mathematics

Research output: Contribution to journal › Review article › peer-review

14 Scopus citations

Abstract

For any prime number k ≥ 3 and any commutative ring A, we describe the subring A_k of A consisting of all sums of kth powers. For some k such as k = 11 or 19, we prove that every element of A_k 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 A_k is the sum of k³t kth powers.

Original language	English (US)
Pages (from-to)	299-307
Number of pages	9
Journal	Journal of Number Theory
Volume	26
Issue number	3
DOIs	https://doi.org/10.1016/0022-314X(87)90086-2
State	Published - Jul 1987

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/0022-314X(87)90086-2

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title = "Waring's problem for commutative rings",

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.",

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AU - Vaserstein, L. N.

N1 - Funding Information: encouragement and some references, S. Simpson Science Foundation for a partial support during

PY - 1987/7

Y1 - 1987/7

N2 - 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.

AB - 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.

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U2 - 10.1016/0022-314X(87)90086-2

DO - 10.1016/0022-314X(87)90086-2

M3 - Review article

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SP - 299

EP - 307

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 3

ER -

Waring's problem for commutative rings

Abstract

All Science Journal Classification (ASJC) codes

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