A Class Of Abelian Groups

Abstract

1. Introduction. If M is any finite set we define a chain on M as a mapping f of M into the set of ordinary integers. If a ∈ M then f (a) is the coefficient of a in the chain f. The set of all a ∈ M such that f (a) ≠ 0 is the domain | f | of f. If | f | is null, that is if f (a) = 0 for all a , then f is the zero chain on M. If M is null it is convenient to say that there is just one chain, a zero chain, on M.