Necklace ring
In mathematics, the necklace ring is a ring introduced by  to elucidate the multiplicative properties of necklace polynomials. Definition

If A is a commutative ring then the necklace ring over A consists of all infinite sequences  of elements of A. Addition in the necklace ring is given by pointwise addition of sequences. Multiplication is given by a sort of arithmetic convolution: the product of  and  has components

where  is the least common multiple of  and , and  is their greatest common divisor. This ring structure is isomorphic to the multiplication of formal power series written in "necklace coordinates": that is, identifying an integer sequence  with the power series . See also

 Witt vector

References

Ring theory