Let G be an abelian group and let Z G be its integral group ring. In special cases (e.g., G finite [4]) it has been noted that G is a direct summand of ( Z G) ∗, the group of units of Z G. However, no explicit construction for the splitting maps is given in the literature. In Section 1 it will be shown that for any abelian group G, there is a canonical splitting of the inclusion G→ Z G ∗. Upon attempting to generalize this result to other coefficient rings, we are led to the concept of a semimodule. We show in Section 2 that G→(AG) ∗ splits if G admits a semimodule structure over A. The final section contains a number of partial results and examples showing the difficulty of deciding whether or not splittings exist in the general case. This paper originated from the construction of maps in algebraic K-theory using the Hochschild homology of a bimodule [6, Chap.X]. Let G→GL n Z G be given by gdiag ( g, 1,…, 1). It will be shown elsewhere that for an arbitrary group G, there is a canonical splitting of the induced map H i(G; Z )→H i(GL n( Z G); Z ) (ordinary homology of groups with trivial action on Z for all i ⩾ 0, n ⩾ 1. As the case i = n = 1 is of independent interest, we present it here rather than obscure it in a paper dealing with algebraic K-theory. For a given integer i, the splitting is constructed via properties of Hochschild homology groups H i ( R, R) for certain rings R. For i = 1 and R a commutative ring, H 1( R, R) is canonically isomorphic to Ω 1 R Z , the module of Kahler differentials. In Section 1 we use Ω 1 R Z and its properties to construct splittings as it will be more familiar than Hochschild homology groups to most readers.