This research is concerned with problems in abelian group theory and in the theory of modules over commutative domains. Several problems on Butler groups will be considered, as well as problems on the torsion product of groups. The principal investigator will also investigate modules over valuation domains. An in-depth study of modules over general domains will be undertaken with special emphasis on the situation when the field of quotients has projective dimension 1. This project has its roots in the theory of abelian groups. Abelian groups are algebraic objects having a commutative multiplicative operation. They arise in a number of areas of mathematics. This research has two basic thrusts. One may have implications for commutative algebra; the second involves the use of logical techniques in the study of abelian groups.
