  Let R be a commutative ring, M an R-module, and N a finitely presented
R-module such that the intersection of Max(R) and Supp(N) is finite-dimensional
and Noetherian. Suppose also that N is homothetic; in other words, suppose that
the natural ring homomorphism from R to the R-endomorphism ring of N is
surjective. Working under these conditions, we describe various ways to
guarantee the existence of a split surjective map in a specified coset of
Hom(M,N). Using these results, we yield an extension of Bass's Cancellation
Theorem that gives sufficient conditions for cancelling N or, more generally, a
direct summand of a direct sum of finitely many copies of N. Since a canonical
module of a Cohen-Macaulay ring is always finitely presented and homothetic,
our work reveals a cancellation property of canonical modules of Cohen-Macaulay
rings with finite-dimensional maximal spectra. Of note is that our results do
not rely on any stable rank conditions.
