Lie ring whose additive group is finitely generated as a module over the ring of integers localized at a set of primes

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Definition

A Lie ring L is termed a Lie ring whose additive group is finitely generated as a module over the ring of integers localized at a set of primes if the additive group of L is an abelian group that is finitely generated as a module over the ring of integers localized at a set of primes. Explicitly: there is a (possibly empty, possibly finite, possibly infinite) subset \pi of the set of prime numbers such that the additive group of L is a finitely generated as a module over the ring \mathbb{Z}[\pi^{-1}]. Another way of putting it is that there is a finite subset S of L such that the \pi-powered subgroup generated by S is the whole group L.