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

Access to Document

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

Cite this

@article{a0ea0002c1bd4a399a982919688ea296,

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.",

author = "Vaserstein, \{L. N.\}",

note = "Funding Information: encouragement and some references, S. Simpson Science Foundation for a partial support during",

year = "1987",

month = jul,

doi = "10.1016/0022-314X(87)90086-2",

language = "English (US)",

volume = "26",

pages = "299--307",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "3",

}

TY - JOUR

T1 - Waring's problem for commutative rings

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.

UR - https://www.scopus.com/pages/publications/38249033375

UR - https://www.scopus.com/pages/publications/38249033375#tab=citedBy

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

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

M3 - Review article

AN - SCOPUS:38249033375

SN - 0022-314X

VL - 26

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

Access to Document

Other files and links

Fingerprint

Cite this