On September 29 and 30 of 1989, Ohio University hosted the Midwest Non- Commutative Ring Theory Conference. With the support of the Office of the Provost for Graduate Programs and Research, the College of Arts and Sciences and the Departments of Mathematics and Computer Science, we were able to bring together speakers from throughout the United States, Canada and the United Kingdom. This volume consists primarily of papers presented by our invited speakers. Some authors who were originally invited but could not attend have also contributed to these proceedings.