Perfect and Semiperfect Rings

Abstract

A bstractThis thesis is essentially an exposition of the standard resu1ts on perfect and semi-perfect rings. Complete characterizations of perfect and sen"li-perfect rings are given in Theorems 1.13 and 2.5 respective1y.A resu1t on commutative perfect rings is obtained in connection with . Conjecture 1.19, which the author consider s to be original. Chapter 3 comprises, in part, a characterization of semi-perfect rings in terms of idempotents and a structure theorem for finite1y-generated projective modules over semi-perfect rings. Finally, in the Appendix, the author formu1ates and discusses a conjecture on subrings of perfect rings. Department of MathematicsMcGill Univer sity The main theorem in Section A of Chapter III characterizes semiperfect rings in terms of idempotents. It has been recognized that much of the c1assical structure theory for Artinian rings can be developed under the weaker hypothesis that R be sem i-perfect.Section B contains some results for perfect and semi-perfect rings which are analogous to those characteristic of Artinian rings.We obtain a decomposition theorem for finitely generated projective modules over semi-perfect rings in Section C. Section