Semiperfect ring

From formulasearchengine
Jump to navigation Jump to search

{{ safesubst:#invoke:Unsubst||$N=Merge to |date=__DATE__ |$B= Template:MboxTemplate:DMCTemplate:Merge partner }}

In abstract algebra, a semiperfect ring is a ring over which every finitely generated left module has a projective cover. This property is left-right symmetric.


Let R be ring. Then R is semiperfect if any of the following equivalent conditions hold:


Examples of semiperfect rings include:


Since a ring R is semiperfect iff every simple left R-module has a projective cover, every ring Morita equivalent to a semiperfect ring is also semiperfect.


  • {{#invoke:citation/CS1|citation

|CitationClass=book }}