Necklace ring

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In mathematics, the necklace ring is a ring introduced by Metropolis and Rota (1983).

Definition[edit]

If A is a commutative ring then the necklace ring over A consists of all infinite sequences (a1,a2,...) 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 (a1,a2,...) and (b1,b2,...) has components

where [i,j] is the least common multiple of i and j, and (i,j) is their highest common factor.

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