Abstract

Fix a set p of prime numbers and let I be the set of integers \(\Bbbk \) relatively prime to the elements of p. An abelian group π is p-local if multiplication by \(\Bbbk \) in π is an isomorphism for all \(\Bbbk \) ∈ I. The rational numbers m/\(\Bbbk \), \(\Bbbk \) ∈ I, are a subring \(\Bbbk \) ⊂ ℚ, so π is P-local if and only if it is a \(\Bbbk \)-module. By convention, when p = o we take \(\Bbbk \) = ℚ — in this case π is a rational vector space. Throughout this section our ground ring k will be the subring associated in this way with the set of primes p.

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