Sums of k-th powers in the Ring of Polynomials with Integer Coefficients

Authors

Ted Chinburg '75, Harvey Mudd College
Melvin Henriksen, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

1976

Abstract

Suppose R is a ring with identity element 1 and k is a positive integer. Let H (k, R) denote the set of kth powers of elements of R, and let J(k, R) denote the additive subgroup of R generated by H(k, R). If Z denotes the ring of integers, then

G(k, R) = {a∊Z: aR ⊆ J(k, R)}

is an ideal of Z.

Rights Information

© 1976 Institutum Mathematicum • Academia Scientiarum Polona

Recommended Citation

Chinburg, Ted; Henriksen, Melvin Sums of k-th powers in the ring of polynomials with integer coefficients. Acta Arith. 29 (1976), no. 3, 227–250.