This volume is an outcomeof invited lecturesdelivered at the Ring Theory Section of the 23rd Ohio State-DenisonConferencein May 1996. It also contains articles by some invited mathematicianswho could not attend the conference. These peer-refereedarticles showcasethe latest developmentsand trends in classicalRing Theory, highlighting the cro- fertilization of new techniquesand ideaswith the existing ones. Providing a wide variety of methodologies,this volume should be valuable both to graduatestudentsas well as to specialistsin Ring Theory. We would like to thank our colleagueswho investeda lot of their time to make the conferencea great success. In particular, our thanks go to ProfessorsTom Dowling, Dan Sanders,SurinderSehgal,Ron Solomonand Sergio R. L6pez-Permouthfor their help. The financial support for the Conference,provided by the Departmentof Mathematics,The Ohio State University, and MathematicsResearchInstitute, Columbus, is gratefully acknowleged. Many thanksgo to Dean Violet I. Meek for her commitment to the promotion of researchby her continuousencouragement of such efforts and for providing financial support from the Lima campusof The Ohio StateUniversity. We havereceivedimmensecooperationfrom all the refereeswho, meticulouslyand in a very short time, provided us with their reports in spite of their busy schedules. We expressour sincerethanks to all of them. Finally, we thank Ms. Cindy White for her excellent job in typing parts of this volume. We are pleasedto dedicatethis volume to ProfessorBruno J. Miiller on the occasionof his retirementfor his many contributionsto the Theory of Rings and Modules. As this volume was going to presswe have learned that ProfessorCarl Faith is retiring this year. This volume is an outcomeof invited lecturesdelivered at the Ring Theory Section of the 23rd Ohio State-DenisonConferencein May 1996. It also contains articles by some invited mathematicianswho could not attend the conference. These peer-refereedarticles showcasethe latest developmentsand trends in classicalRing Theory, highlighting the cro- fertilization of new techniquesand ideaswith the existing ones. Providing a wide variety of methodologies,this volume should be valuable both to graduatestudentsas well as to specialistsin Ring Theory. We would like to thank our colleagueswho investeda lot of their time to make the conferencea great success. In particular, our thanks go to ProfessorsTom Dowling, Dan Sanders,SurinderSehgal,Ron Solomonand Sergio R. L6pez-Permouthfor their help. The financial support for the Conference,provided by the Departmentof Mathematics,The Ohio State University, and MathematicsResearchInstitute, Columbus, is gratefully acknowleged. Many thanksgo to Dean Violet I. Meek for her commitment to the promotion of researchby her continuousencouragement of such efforts and for providing financial support from the Lima campusof The Ohio StateUniversity. We havereceivedimmensecooperationfrom all the refereeswho, meticulouslyand in a very short time, provided us with their reports in spite of their busy schedules. We expressour sincerethanks to all of them. Finally, we thank Ms. Cindy White for her excellent job in typing parts of this volume. We are pleasedto dedicatethis volume to ProfessorBruno J. Miiller on the occasionof his retirementfor his many contributionsto the Theory of Rings and Modules. As this volume was going to presswe have learned that ProfessorCarl Faith is retiring this year.