College of Liberal Arts & Sciences

# Algebra Seminar

**Abstract: **

The concepts of "zero-divisor'' and "nilpotent element'' play an important role in Ring Theory. Various types of rings have been defined to distinguish between rings satisfying certain properties related to zero divisors and nilpotent elements, which include semicommutative, reflexive, 2-primal, NI, McCoy, etc. In this talk, we would like to present some contributions to the hierarchy and interconnections between some of those types of rings. We will mainly focus on characterizations of reflexive and NI rings in the setting of Morita context rings. Using these characterizations, we also provide characterizations of prime, semiprime, 2-primal, and weakly 2-primal rings. It is shown the ring of row and column finite matrices over a reflexive ring is a reflexive non-Dedekind finite ring.