The lattice of quasivarietes of modules over a Dedekind ring

Abstract

In 1995 D. V. Belkin described the lattice of quasivarieties of modules over  principal ideal domains. The following paper provides a description of the lattice of subquasivarieties of the variety of modules over a given Dedekind ring. It also shows which subvarieties of these modules are deductive (a variety is deductive if every subquasivariety is a variety).