Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subr...Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subring which is a subfield containing 1. It is shown that R/NUVW, where U is a finite ring, V is a finite direct sum of matrix rings over B rings, and W is a ring containing no nonzero finite subrings.展开更多
文摘Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subring which is a subfield containing 1. It is shown that R/NUVW, where U is a finite ring, V is a finite direct sum of matrix rings over B rings, and W is a ring containing no nonzero finite subrings.
