THE OSU-OU Ring Theory Seminar


Speaker: Vera Puninskaya

          University of Camerino (ITALY)


Title:  Strongly minimal modules


Day, Date and Time:  Friday, May 30, 4:30 p.m.


Room:  MW 154 (OSU-Columbus campus)



Abstract: An infinite algebraic system $A$ is said to be strongly minimal if any formula with parameters from an elementary extension of $A$ defines in $A$ a finite or cofinite subset. Strongly minimal groups were completely described by Reineke (1975). The main objective of this talk is to give a complete algebraic description of strongly minimal modules over commutative rings, and over right distributive rings. A more precise description was obtained for strongly minimal modules over commutative Pr\"{u}fer rings, and injective strongly minimal modules over commutative rings. There are some results on strongly minimal modules over noncommutative rings. For instance, if there exists a faithful strongly minimal module over a ring $R$, then $R$ is a domain embeddable in a skew field.