Structure of certain rings with conditions on nonperiodic elements and certain Von Neumann Π-regular rings with prime centers

Abstract

First, we study the structure and commutativity of rings with the property that for each nonperiodic element x, there exists a positive integer K=K(x), such that x^k is central for all k>K. Then we study rings with certain conditions on zero divisors, for example we prove that a periodic ring with identity and commuting nilpotents, such that every zero divisor is either idempotent or nilpotent, then N is an ideal and R/N is either Boolean or a field. We also study rings with prime or semi prime center, in particular we study the structure of certain Von-Neumann Π-regular rings with certain constraints such as having prime centers and other constraints. The structure of rings with other conditions on elements will also be studied. (Please note that the results in this thesis are essentially based on papers: [1], [2], [3], [4])