Decompositions of Algebraically Compact Modules

This paper is mainly concerned with describing the category of all algebraically compact (= pure-injective) modules. A family of functors from this category to categories of injective modules, that is, spectral categories, is defined. Via these functors we transfer the decompositions of the objects of a spectral category and their invariants to algebraically compact modules. For instance, as a corollary we find the decompositions and the invariants for algebraically compact abelian groups and the decompositions for algebraically compact modules over Prüfer rings. Our results yield a connection between the theory of algebraically compact modules and the one of injective modules. © 1985 by Pacific Journal of Mathematics.