May modules of countable rank

Abstract

In a 1990 paper, W. May studied the question of when isomorphisms of the endomorphism rings of mixed modules are necessarily induced by isomorphisms of the underlying modules. In so doing he introduced a class of mixed modules over a complete discrete valuation domain; we later renamed these modules after their inventor. The class of May modules of countable torsion-free rank is particularly important. A decomposition theorem is established for such modules. The modules in this class are characterized in several ways. Finally, an example is constructed showing that several of these ideas do not extend to May modules of uncountable torsion-free rank.