Cyclotomic Completions of Polynomial Rings

  • Kazuo Habiro

    Kyoto University, Japan


For a subset and a commutative ring with unit, let denote the completion , where runs over all the products of the powers of cyclotomic polynomials with . We will show that under certain conditions the completion can be regarded as a “ring of analytic functions” defined on the set of roots of unity of order in . This means that an element of vanishes if it vanishes on a certain type of infinite set of roots of unity, or if its power series expansion at one root of unity vanishes. In particular, the completion enjoys this property.

Cite this article

Kazuo Habiro, Cyclotomic Completions of Polynomial Rings. Publ. Res. Inst. Math. Sci. 40 (2004), no. 4, pp. 1127–1146

DOI 10.2977/PRIMS/1145475444